1. The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
a) 7 : 3
b) 5 : 2
c) 13 : 4
d) 9 : 2
Discussion
Explanation: Let the ages of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
⇒ 3x + 20 = 2x + 40
⇒ x = 20
∴ Required ratio
= (3x + 10) : (x + 10)
= 70 : 30
= 7 : 3
2. The ages of Shakti and Kanti are in the ratio of 8 : 7 respectively. After 10 years, the ratio of their ages will be 13 : 12. What is the difference between their ages ?
a) 4 Years
b) 6 Years
c) 2 Years
d) 8 Years
Discussion
Explanation: Let Shakti's age be 8$$x$$ years,
Then Kanti's age = 7$$x$$ years
$$\eqalign{ & \therefore \frac{{8x + 10}}{{7x + 10}} = \frac{{13}}{{12}} \cr & \Rightarrow 12\left( {8x + 10} \right) = 13\left( {7x + 10} \right) \cr & \Rightarrow 96x + 120 = 91x + 130 \cr & \Rightarrow 5x = 10 \cr & \Rightarrow x = 2 \cr} $$
Difference between their ages
$$\eqalign{ & = \left( {8x - 7x} \right) \cr & = {\text{ }}x\,{\text{years}} \cr & {\text{ = 2}}\,{\text{years}} \cr} $$
3. At present Suresh's age is twice the age of his daughter. After 6 year from now, the ratio of the ages of Suresh and his daughter will be 23 : 13. What is the present age of Suresh ?
a) 36 years
b) 40 years
c) 46 years
d) Cannot be determined
Discussion
Explanation: Let daughter's age be x years.
Suresh's age = 2x years
$$\eqalign{ & \therefore \frac{{2x + 6}}{{x + 6}} = \frac{{23}}{{13}} \cr & 13\left( {2x + 6} \right) = 23\left( {x + 6} \right) \cr & 26x + 78 = 23x + 138 \cr & 3x = 60 \cr & x = 20 \cr} $$
Present age of Suresh = 2x years
$$\eqalign{ & {\text{ = }}\left( {2 \times 20} \right){\text{ years }} \cr & {\text{ = 40 years}} \cr} $$
4. A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
a) 32 years
b) 36 years
c) 40 years
d) 48 years
Discussion
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{mother's}}\,{\text{present}}\,{\text{age}}\,{\text{be}}\,x\,{\text{years}}{\text{.}} \cr & {\text{Then,}}\,{\text{the}}\,{\text{person's}}\,{\text{present}}\,{\text{age}} \cr & = {\frac{2}{5}x} \,\,{\text{years}} \cr & {\frac{2}{5}x + 8} = \frac{1}{2}\left( {x + 8} \right) \cr & 2\left( {2x + 40} \right) = 5\left( {x + 8} \right) \cr & x = 40 \cr} $$
5. The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:
a) 12 years
b) 14 years
c) 18 years
d) 20 years
Discussion
Explanation: Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
54 - x = 5x - 30
6x = 84
x = 14
Son's age after 6 years = (x + 6) = 20 years.
6. The present age of Mr. Sanyal is three times the age of his son. Six years hence , the ratio of their ages will be 5 : 2. What is the present age of Mr. Sanyal ?
a) 60 years
b) 54 years
c) 48 years
d) 50 years
Discussion
Explanation: Let the son's age be $$x$$ years ,
Then Mr. Sanyal's age = 3$$x$$ years
$$\eqalign{ & \therefore \frac{{3x + 6}}{{x + 6}} = \frac{5}{2} \cr & \Rightarrow 2\left( {3x + 6} \right) = 5\left( {x + 6} \right) \cr & \Rightarrow 6x + 12 = 5x + 30 \cr & \Rightarrow x = 18 \cr} $$
∴ Present age of Mr. Sanyal = 3x years
= (3 × 18) years
= 54 years
7. Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
a) 6 years
b) 2 years
c) 8 years
d) 4 years
Discussion
Explanation: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.
∴ Required difference = (42 - 36) years = 6 years.
8. The ages of Nitish and Vinnee are in the ratio 6 : 5 respectively. After 9 years the ratio of their ages will be 9 : 8. What is the difference in their ages now ?
a) 9 Years
b) 7 Years
c) 3 Years
d) 5 Years
Discussion
Explanation: Let Nishi's age be 6x years,
Then Vinnee's age = 5x years
$$\eqalign{ & \therefore \frac{{6x + 9}}{{5x + 9}} = \frac{9}{8} \cr & \Rightarrow 8\left( {6x + 9} \right) = 9\left( {5x + 9} \right) \cr & \Rightarrow 48x - 45x = 81 - 72 \cr & \Rightarrow 3x = 9 \cr & \Rightarrow x = 3 \cr & {\text{Difference in their ages}} \cr & {\text{ = }}\left( {6x - 5x} \right) \cr & = x {\text{ years}} \cr & = {\text{3 years}} \cr} $$
9. At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?
a) 12 years
b) 15 years
c) 19 and half
d) 21 years
Discussion
Explanation: Let the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,
4x + 6 = 26
x = 20
x = 5
Deepak's age = 3x = 15 years.
10. The age of a mother today is thrice that of her daughter. After 12 years , the age of the mother will be twice that of her daughter. The present age of the daughter is = ?
a) 12 Years
b) 14 Years
c) 18 Years
d) 16 Years
Discussion
Explanation: Let the daughter's age be x years.
Then, mother age = 3x years
3x + 12 = 2 (x + 12)
3x + 12 = 2x + 24
x = 12
Present age of daughter = 12 years
11. The average of the ages of a man and his daughter is 34 years. If the respective ratio of their ages four years from now is 14 : 5,what is daughter's present age ?
a) 12 years
b) 10 years
c) 18 years
d) 16 years
Discussion
Explanation: Average age of man and his daughter = 34 years
Their total age = (34 × 2) years = 68 years
Let man's age be x years,
Then daughter age = (68 - x) years
$$\eqalign{ & \therefore \frac{{x + 4}}{{68 - x + 4}} = \frac{{14}}{5} \cr & \Rightarrow 5\left( {x + 4} \right) = 14\left( {72 - x} \right) \cr & \Rightarrow 5x + 20 = 1008 - 14x \cr & \Rightarrow 19x = 988 \cr & \Rightarrow x = 52 \cr} $$
∴ Daughter's present age
= (68 - 52) years
= 16 years
12. Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?
a) 24.5 years
b) 28 years
c) 16 years
d) 18 years
Discussion
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{Rahul's}}\,{\text{age}}\,{\text{be}}\,x\,{\text{years}}. \cr & {\text{Then,}}\,{\text{Sachin's}}\,{\text{age}} = \left( {x - 7} \right)\,{\text{years}}. \cr & \therefore \frac{{x - 7}}{x} = \frac{7}{9} \cr & \Rightarrow 9x - 63 = 7x \cr & \Rightarrow 2x = 63 \cr & \Rightarrow x = 31.5 \cr & {\text{Hence,}}\,{\text{Sachin's}}\,{\text{age}} \cr & = \left( {x - 7} \right)\,{\text{years}} \cr & = 24.5\,{\text{years}} \cr} $$
13. Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?
a) 1 year
b) 2 years
c) 25 years
d) Data inadequate
Discussion
Explanation: Given that:
1. The difference of age b/w R and Q = The difference of age b/w Q and T.
2. Sum of age of R and T is 50 i.e. (R + T) = 50.
Question: R - Q = ?
R - Q = Q - T
(R + T) = 2Q
Now given that, (R + T) = 50
So, 50 = 2Q and therefore Q = 25.
Question is (R - Q) = ?
Here we know the value(age) of Q (25), but we don't know the age of R.
Therefore, (R-Q) cannot be determined.
14. The ages of A and B are in the ratio 6 : 5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years ?
a) 9 : 8
b) 3 : 4
c) 8 : 7
d) 7 : 6
Discussion
Explanation:
$$\eqalign{ & {\text{A's age = }}\left( {44 \times \frac{6}{{11}}} \right){\text{years}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 24 years}} \cr & {\text{and B's age = }}\left( {44 - 24} \right){\text{years}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 20 years}} \cr} $$
Ratio of their ages after 8 years
$$\eqalign{ & {\text{ = }}\frac{{\left( {24 + 8} \right)}}{{\left( {20 + 8} \right)}} \cr & = \frac{{32}}{{28}} \cr & = \frac{8}{7} \cr & = 8:7 \cr} $$
15. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
a) 20 years
b) 22 years
c) 18 years
d) 14 years
Discussion
Explanation: Let the son's present age be x years. Then, man's present age = (x + 24) years.
∴ (x + 24) + 2 = 2(x + 2)
⇒ x + 26 = 2x + 4
⇒ x = 22
16. Ten years ago, a man was seven times as old as his son. Two years hence, twice his age will be equal to five times the age of his son. What is the present age of the son ?
a) 12 years
b) 13 years
c) 14 years
d) 15 years
Discussion
Explanation: Let son's age 10 years ago be x years.
Then, man's age 10 years ago = 7x years
Son's present age = (x + 10) years,
Man's present age = (7x + 10) years
$$\eqalign{ & {\text{2}}\left[ {\left( {7x + 10} \right) + 2} \right]{\text{ = 5}}\left[ {\left( {x + 10} \right) + 2} \right] \cr & 2\left( {7x + 12} \right) = 5\left( {x + 12} \right) \cr & 14x + 24 = 5x + 60 \cr & 9x = 36 \cr & x = 4 \cr} $$
Son's present age = (x + 10) years
= (4 + 10) years
= 14 years
17. The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
a) 16, 28, 36
b) 20, 35, 45
c) 8, 20, 28
d) None of these
Discussion
Explanation: Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
⇒ 20x = 80
⇒ x = 4
Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.
18. Farah got married 8 years ago, Today her age is $$1\frac{2}{7}$$ times her age at the time of her marriage. At present her daughter's age is one-sixth of her age. What was her daughter's age 3 years ago ?
a) 4 Years
b) 3 Years
c) 6 Years
d) Cannot be determind
Discussion
Explanation: Let Farah's age 8 years ago be x years.
Then , her present age = (x + 8)
$$\eqalign{ & x + 8 = \frac{9}{7}x \cr & 7x + 56 = 9x \cr & 2x = 56 \cr & x = 28 \cr} $$
∴ Farah's age now
= (x + 8) years
= (28 + 8) years
= 36
Her daughter's age now
=$$\left( {\frac{1}{6} \times 36} \right)$$ years
= 6 years
Her daughter's age 3 years ago
= (6 - 3) years
= 3 years
19. The ages of Samina and Suhana are in the ratio of 7 : 3 respectively. After 6 years, the ratio of their ages will be 5 : 3. What is the difference in their ages?
a) 10 years
b) 6 years
c) 12 years
d) 8 years
Discussion
Explanation: Let Samina's age be 7x years.
Then, Suhana's age = 3x years
$$\eqalign{ & \therefore \frac{{7x + 6}}{{3x + 6}} = \frac{5}{3} \cr & \Rightarrow 3\left( {7x + 6} \right) = 5\left( {3x + 6} \right) \cr & \Rightarrow 21x + 18 = 15x + 30 \cr & \Rightarrow 6x + 12 \cr & \Rightarrow x = 2 \cr} $$
Difference in their ages = (7x - 3x) years
= 4x years
= (4 × 2) years
= 8 years
20. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
a) 16 years
b) 18 years
c) 20 years
d) Cannot be determined
Discussion
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{ages}}\,{\text{of}}\,{\text{Kunal}}\,{\text{and}}\,{\text{Sagar}}\,{\text{6}}\,{\text{years}}\,{\text{ago}}\, \cr & {\text{be}}\,6x\,{\text{and}}\,5x\,{\text{years}}\,{\text{respectively}} \cr & \frac{{\left( {6x + 6} \right) + 4}}{{\left( {5x + 6} \right) + 4}} = \frac{{11}}{{10}} \cr & 10\left( {6x + 10} \right) = 11\left( {5x + 10} \right) \cr & 5x = 10 \cr & x = 2 \cr & {\text{Sagar's}}\,{\text{present}}\,{\text{age}} \cr & = \left( {5x + 6} \right)\,{\text{years}} \cr & = 16\,{\text{years}}\, \cr} $$
21. The ratio between the parents ages of A and B is 5 : 3 respectively. The ratio between A's age 4 years ago and B's 4 years hence is 1 : 1. What is the ratio between A's age 4 years hence and B's age 4 years ago ?
a) 1 : 3
b) 3 : 1
c) 2 : 1
d) 4 : 1
Discussion
Explanation: Let A's age be 5x years, then B's age = 3x years
$$\eqalign{ & \frac{{5x - 4}}{{3x + 4}} = \frac{1}{1} \cr & 5x - 4 = 3x + 4 \cr & 2x = 8 \cr & x = 4 \cr & \frac{{{\text{A's age 4 years hence}}}}{{{\text{B's age 4 years ago }}}} \cr & = \frac{{5x + 4}}{{3x - 4}} \cr & = \frac{{5 \times 4 + 4}}{{3 \times 4 - 4}} \cr & = \frac{{24}}{8} \cr & = \frac{3}{1} \cr & = 3:1 \cr} $$
22. The ratio between the ages of Neelam and Shiny is 5 : 6 respectively. If the ratio between the one-third age of Neelam and half of Shiny's age is 5 : 9, then what is Shiny's age = ?
a) 25 years
b) 30 years
c) 36 years
d) Cannot be determined
Discussion
Explanation: Let Neelam's age be 5x years and Shiny's age be 6x years
$$\eqalign{ & \left( {\frac{1}{3} \times 5x} \right):\left( {\frac{1}{2} \times 6x} \right) = 5:9 \cr & \frac{{5x}}{{3 \times 3x}} = \frac{5}{9} \cr} $$
Shiny's age cannot be determined
23. 18 years ago, a man was three times as old as his son. Now, the man is twice as old as his son. The sum of the present ages of the man and his son is =
a) 54 year
b) 72 years
c) 105 years
d) 108 years
Discussion
Explanation: Let the son's age 18 years ago be x years,
Then man's age 18 years ago = 3x years
$$\eqalign{ & \left( {3x + 18} \right) = 2\left( {x + 18} \right) \cr & 3x + 18 = 2x + 36 \cr & x = 18 \cr} $$
Sum of their present ages
$$\eqalign{ & \left( {3x + 18 + x + 18} \right){\text{years}} \cr & \left( {4x + 36} \right){\text{years}} \cr & \left( {4 \times 18 + 36} \right){\text{years}} \cr & {\text{ 108 years}} \cr} $$
24. The age of a man 10 years ago was thrice the age of his son. 10 years hence, the man's age will be twice the age of his son. The ratio of their present ages is = ?
a) 5 : 2
b) 7 : 3
c) 9 : 2
d) 13 : 4
Discussion
Explanation: Let son's age 10 years ago be x years,
Then man's age 10 years ago = 3x years
Son's present age = (x + 10) years
Man's present age = (3x + 10) years
$$\eqalign{ & \left( {3x + 10} \right) + 10 = 2\left( {x + 10 + 10} \right) \cr & 3x + 20 = 2\left( {x + 20} \right) \cr & 3x + 20 = 2x + 40 \cr & x = 20 \cr} $$
Ratio of present ages of man and the son
$$\eqalign{ & {\text{ = }}\frac{{3x + 10}}{{x + 10}} \cr & = \frac{{3 \times 20 + 10}}{{20 + 10}} \cr & = \frac{{70}}{{30}} \cr & = 7:3 \cr} $$
25. Tanya's grandfather was 8 times older to her 16 years ago. He would be 3 times of her age 8 years from now. 8 years ago, what was the ratio of Tanya's age to that of her grandfather ?
a) 1 : 2
b) 1 : 5
c) 3 : 8
d) None of these
Discussion
Explanation: 16 years ago, let T = x years and G = 8x years
After 8 years from now,
T = (x + 16 + 8) years and G = (8x + 16 + 8) years
$$\eqalign{ & {\text{8x + 24 = 3}}\left( {x + 24} \right) \cr & 8x - 3x = 72 - 24 \cr & 5x = 48 \cr & 8{\text{years ago,}} \cr & {\text{ }}\frac{{\text{T}}}{{\text{G}}} \cr & = \frac{{x + 8}}{{8x + 8}} \cr & = \frac{{\frac{{48}}{5} + 8}}{{8 \times \frac{{48}}{5} + 8}} \cr & = \frac{{48 + 40}}{{384 + 40}} \cr & = \frac{{88}}{{424}} \cr & = \frac{{11}}{{53}} \cr} $$
26. Rajan got married 8 years ago. His present age is $$\frac{6}{5}$$ times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marrige. The age of Rajan's sister is =
a) 32 years
b) 36 years
c) 38 years
d) 40 years
Discussion
Explanation: Let Rajan's age 8 years ago be x years,
Present age = (x + 8) years
$$\eqalign{ & x + 8 = \frac{6}{5}x \cr & 5x + 40 = 6x \cr & x = 40 \cr} $$
Rajan's sister's age 8 years ago
= (40 - 10) years
= 30 years
His sister's age now
= (30+8) years
= 38 years
27. A couple has a son and a daughter. The age of the father is four times that of the son and the age of the daughter is one-third of that of her mother. The wife is 6 years younger to her husband and the sister is 3 years older then her brother. The mother's age is = ?
a) 42 years
b) 48 years
c) 54 years
d) 63 years
Discussion
Explanation: M → Mother, F → Father, S → Son and D → Daughter
F = 4S, D = $$\frac{1}{3}$$M, M = F - 6 and S = D - 3
$$\eqalign{ & M = 3D = 3\left( {S + 3} \right) \cr & = 3S + 9 = \frac{3}{4}F + 9 = \frac{3}{4}\left( {M + 6} \right) + 9 \cr & = \frac{3}{4}M + \frac{3}{4} \times 6 + 9 \cr & \Rightarrow \left( {M - \frac{3}{4}M} \right) = \left( {\frac{9}{2} + 9} \right) \cr & \Rightarrow \frac{1}{4}M = \frac{{27}}{2} \cr & \Rightarrow M = \left( {\frac{{27}}{2} \times 4} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 54\,{\text{years}} \cr} $$
28. Reenu's father was 38 years of age when she was born while her mother was 36 years old when her brother 4 years younger to her was born. What is the difference between the ages of her parents ?
a) 2 Years
b) 4 Years
c) 6 Years
d) 8 years
Discussion
Explanation: Mother's age when Reenu's brother was born = 36 year
Father's age when Reenu's brother was born = (38 + 4) years = 42 year
Required difference = (42 - 36) years = 6 years
29. A man was asked to state his age in years. His reply was, "Take my age 3 years hence, multiply it by 3 and then subtract 3 times my age 3 years ago and you will know how old I am". What is the age of the man ?
a) 18 years
b) 20 years
c) 24 years
d) 32 years
Discussion
Explanation: Let the present age of the man be x years
$$\eqalign{ & {\text{3}}\left( {x + 3} \right) - 3\left( {x - 3} \right) = x \cr & \left( {3x + 9} \right) - \left( {3x - 9} \right) = x \cr & x = 18 \cr} $$
The present age of the man is 18 years
30. The ratio of a man's age and his son's age is 7 : 3 and the product of their ages is 756. The ratio of their ages after 6 years will be ?
a) 5 : 2
b) 2 : 1
c) 11 : 7
d) 13 : 9
Discussion
Explanation: Let the man's age be 7x years
Then son's age = 3x years
$$\eqalign{ & {\text{7}}x \times 3x = 756 \cr & 21{x^2} = 756 \cr & {x^2} = 756 \cr & {x^2} = 36 \cr & x = 6 \cr} $$
The ratio of their ages after 6 years
$$\eqalign{ & {\text{ = }}\left( {7x + 6} \right):\left( {3x + 6} \right) \cr & = \left( {7 \times 6 + 6} \right):\left( {3 \times 6 + 6} \right) \cr & = 48:24 \cr & = 2:1 \cr} $$
31. Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?
a) 2 times
b) $$2\frac{1}{2}\,{\text{times}}$$
c) $$2\frac{3}{4}\,{\text{times}}$$
d) 3 times
Discussion
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{Ronit's}}\,{\text{present}}\,{\text{age}}\,{\text{be}}\,x\,{\text{years}}. \cr & {\text{Father's}}\,{\text{present}}\,{\text{age}}\, = \left( {x + 3x} \right)\,{\text{years}} \cr & = 4x\,{\text{years}} \cr & \left( {4x + 8} \right) = \frac{5}{2}\left( {x + 8} \right) \cr & 8x + 16 = 5x + 40 \cr & 3x = 24 \cr & \Rightarrow x = 8 \cr & {\text{Required}}\,{\text{times}} \cr & = \frac{{ {4x + 16} }}{{ {x + 16} }} \cr & = \frac{{48}}{{24}} \cr & = 2 \cr} $$
32. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
a) 4 years
b) 8 years
c) 10 years
d) None of these
Discussion
Explanation: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4
33. A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
a) 14 years
b) 19 years
c) 33 years
d) 38 years
Discussion
Explanation: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
34. A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
a) 7
b) 8
c) 9
d) 10
Discussion
Explanation: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25
x = 5
B's age = 2x = 10 years.
35. Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
a) 24
b) 27
c) 40
d) None of these
Discussion
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{present}}\,{\text{ages}}\,{\text{of}}\,{\text{Sameer}}\,{\text{and}}\,{\text{Anand}}\,{\text{be}}\, 5x\,{\text{years}}\,{\text{and}}\,4x\,{\text{years}}\,{\text{respectively}} \cr & \frac{{5x + 3}}{{4x + 3}} = \frac{{11}}{9} \cr & 9\left( {5x + 3} \right) = 11\left( {4x + 3} \right) \cr & 45x + 27 = 44x + 33 \cr & 45x - 44x = 33 - 27 \cr & x = 6 \cr & {\text{Anand's}}\,{\text{present}}\,{\text{age}} \cr & = 4x \cr & = 24\,{\text{years}}\, \cr} $$
36. 6 years ago , the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present ?
a) 16 years
b) 18 years
c) 20 years
d) Cannot be determined
Discussion
Explanation: Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years
$$\eqalign{ & \frac{{\left( {6x + 6} \right) + 4}}{{\left( {5x + 6} \right) + 4}} = \frac{{11}}{{10}} \cr & \frac{{6x + 10}}{{5x + 10}} = \frac{{11}}{{10}} \cr & 10\left( {6x + 10} \right) = 11\left( {5x + 10} \right) \cr & 60x + 100 = 55x + 100 \cr & 5x = 10 \cr & x = 2 \cr} $$
Sagar's present age
= (5x + 6) years
= (5 × 2 + 6) years
= 16 years
37. Sneh's age is $$\frac{1}{6}$$ th of her father's age. Sneh's father's age will be twice of Vimal's age after 10 years. If Vimal's 8th birthday was celebrated 2 years ago,then what is Sneh's present age ?
a) $${\text{6}}\frac{2}{3}{\text{ }}$$ years
b) 10 years
c) 12 years
d) 15 years
Discussion
Explanation: Vimal's present age = (8 + 2) years
= 10 years
Sneh's father's age = 2(10 + 10) years
= 40 years
Sneh's age
$$\eqalign{ & {\text{ = }}\left( {\frac{1}{6} \times 40} \right){\text{ years }} \cr & {\text{ = }}\frac{{20}}{3}{\text{years }} \cr & {\text{ = 6}}\frac{2}{3}{\text{years}} \cr} $$
38. The ages of Sulekha and Arunima are in the ratio 9 : 8 respectively. After 5 years, the ratio of their ages will be 10 : 9. What is the difference in their ages ?
a) 4 Years
b) 5 Years
c) 6 Years
d) 7 years
Discussion
Explanation: Let Sulekha age be 9 year,
Arunima's age = 8x years
$$\eqalign{ & \frac{{9x + 5}}{{8x + 5}} = \frac{{10}}{9} \cr & 9\left( {9x + 5} \right) = 10\left( {8x + 5} \right) \cr & 81x + 45 = 80x + 50 \cr & x = 5 \cr} $$
Difference in their ages
= (9x - 8x) years
= x years
= 5 years
39. X's age 3 years ago was three times the present age of Y. At present Z's age is twice the age of Y. Also Z is 12 years younger than X. What is the present age of Z ?
a) 15 years
b) 24 years
c) 12 years
d) 18 years
Discussion
Explanation: Let the present age of Y be a years
Three years ago X's age = 3a years
Then, present age of X is (3a + 3)
Z's present age = 2a
Now, (3a + 3) - 2a = 12
a = 9 year
Present age of Z = 2a = 2 × 9 = 18 years
40. Eight year ago, Poorvi's age was equal to the sum of the present ages of her one son and one daughter. Five years hence, the respective ratio between the ages of her daughter and her son that time will be 7 : 6. If Poorvi's husband is 7 years elder to her and his present age is three times the present age of their son, what is the present age of the daughter ? (in year)
a) 15 years
b) 23 years
c) 19 years
d) 27 years
Discussion
Explanation: Let the age of the son and the daughter of Poorvi be 6a years and 7a years respectively.
5 years hence, present age of son = 6a - 5 and present age of daughter = 7a - 5
Eight years ago, the age of Poorvi = 6a - 5 + 7a - 5 = 13a - 10
So, present age of Poorvi = 13a - 10 + 8 = 13a - 2
Since, present age of Poorvi husband = 3 (6a - 5)
The difference of present age of Poorvi husband and Poorvi = 7 (Given)
$$\eqalign{ & {\text{3}}\left( {6a - 5} \right) - \left( {13a - 2} \right) = 7 \cr & 18a - 15 - 13a + 2 = 7 \cr & 5a = 20 \cr & a = 4 \cr} $$
The present age of daughter
= (7a - 5)
= 7 × 4 - 5
= 23 years