1. 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
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
2. 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
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{Rahul's}}\,{\text{age}}\,{\text{be}}\,x\,{\text{years}}. \cr & {\text{Then,}}\,{\text{Sachin's}}\,{\text{age}} = \left( {x - 7} \right)\,{\text{years}}. \cr & \therefore \frac{{x - 7}}{x} = \frac{7}{9} \cr & \Rightarrow 9x - 63 = 7x \cr & \Rightarrow 2x = 63 \cr & \Rightarrow x = 31.5 \cr & {\text{Hence,}}\,{\text{Sachin's}}\,{\text{age}} \cr & = \left( {x - 7} \right)\,{\text{years}} \cr & = 24.5\,{\text{years}} \cr} $$
3. 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
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.
4. 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
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
$$\eqalign{ & {\text{ = }}\frac{{\left( {24 + 8} \right)}}{{\left( {20 + 8} \right)}} \cr & = \frac{{32}}{{28}} \cr & = \frac{8}{7} \cr & = 8:7 \cr} $$
5. 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
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
6. 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
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
7. 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
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.
8. 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
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
9. 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
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
10. 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
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{ages}}\,{\text{of}}\,{\text{Kunal}}\,{\text{and}}\,{\text{Sagar}}\,{\text{6}}\,{\text{years}}\,{\text{ago}}\, \cr & {\text{be}}\,6x\,{\text{and}}\,5x\,{\text{years}}\,{\text{respectively}} \cr & \frac{{\left( {6x + 6} \right) + 4}}{{\left( {5x + 6} \right) + 4}} = \frac{{11}}{{10}} \cr & 10\left( {6x + 10} \right) = 11\left( {5x + 10} \right) \cr & 5x = 10 \cr & x = 2 \cr & {\text{Sagar's}}\,{\text{present}}\,{\text{age}} \cr & = \left( {5x + 6} \right)\,{\text{years}} \cr & = 16\,{\text{years}}\, \cr} $$