1. 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
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{Ronit's}}\,{\text{present}}\,{\text{age}}\,{\text{be}}\,x\,{\text{years}}. \cr & {\text{Father's}}\,{\text{present}}\,{\text{age}}\, = \left( {x + 3x} \right)\,{\text{years}} \cr & = 4x\,{\text{years}} \cr & \left( {4x + 8} \right) = \frac{5}{2}\left( {x + 8} \right) \cr & 8x + 16 = 5x + 40 \cr & 3x = 24 \cr & \Rightarrow x = 8 \cr & {\text{Required}}\,{\text{times}} \cr & = \frac{{ {4x + 16} }}{{ {x + 16} }} \cr & = \frac{{48}}{{24}} \cr & = 2 \cr} $$
2. 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
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
3. 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
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.
4. 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
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.
5. 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
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{present}}\,{\text{ages}}\,{\text{of}}\,{\text{Sameer}}\,{\text{and}}\,{\text{Anand}}\,{\text{be}}\, 5x\,{\text{years}}\,{\text{and}}\,4x\,{\text{years}}\,{\text{respectively}} \cr & \frac{{5x + 3}}{{4x + 3}} = \frac{{11}}{9} \cr & 9\left( {5x + 3} \right) = 11\left( {4x + 3} \right) \cr & 45x + 27 = 44x + 33 \cr & 45x - 44x = 33 - 27 \cr & x = 6 \cr & {\text{Anand's}}\,{\text{present}}\,{\text{age}} \cr & = 4x \cr & = 24\,{\text{years}}\, \cr} $$
6. 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
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
7. 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
Explanation: Vimal's present age = (8 + 2) years
= 10 years
Sneh's father's age = 2(10 + 10) years
= 40 years
Sneh's age
$$\eqalign{ & {\text{ = }}\left( {\frac{1}{6} \times 40} \right){\text{ years }} \cr & {\text{ = }}\frac{{20}}{3}{\text{years }} \cr & {\text{ = 6}}\frac{2}{3}{\text{years}} \cr} $$
8. 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
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
9. 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
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
10. 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
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