## Problem on Ages Questions and Answers Part-4

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

\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}