Problems on Ages - 2

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9. Jayesh is as much younger to Anil as he is older to Prashant. If the sum of the ages of Anil and Prashant is 48 years, what is the age of Jayesh?
a. 20 years
b. 24 years
c. 30 years
d. Cannot be determined

Answer: B
Explanation:
$P < J < A$
The given question says the difference between Anil and Jayesh is same as Jayesh and Prashant
$\therefore $ $A - J = J - P$
$\Rightarrow 2J = A + P$
Given $A + P = 48$
$\therefore $ $2J = 48 $
$\Rightarrow J = 24$

Alternate Method:
Let Anil's age = $x$ years. Then, Prasant's age = $(48 - x)$ years.
Let the age of Jayesh be $J$ years
$A - J = J - P $
$ \Rightarrow $ $J - (48 - x) = x - P $
$\Rightarrow 2P = 48$
$ \Rightarrow P = 24$

10. Three years ago the average age of A and B was 18 years. With C joining them, the average becomes 22 years. How old is C now ?
a. 24 years
b. 27 years
c. 28 years
d. 30 years

Answer: A
Explanation:
Present average age of A and B = $(18 + 3) = 21$ years.
Sum of ages of A,B now = $(21 \times 2) = 42$ years.
Sum of ages of A, B and C, now = $(22 \times 3) = 66$ years.
C's age $= (66 - 42) = 24$ years

11. One year ago the ratio between Samir and Ashok's age was 4:3. One year hence the ratio of their age will be 5:4. What is the sum of their present ages in years?
a. 12 years
b. 15 years
c. 16 years
d. Cannot be determined.

Answer: C
Explanation:
$\begin{array}{*{20}{|c|cc|}} \hline
{}&{Samir}&{Ashok} \\ \hline
\text{1 year ago ages}&{4x}&{3x} \\ \hline
\text{Present ages}&{4x+1}&{3x+1} \\ \hline
\text{1 year hence ages}&{4x+2}&{3x+2} \\ \hline
\end{array}$
$\displaystyle\frac{{4x + 2}}{{3x + 2}} = \displaystyle\frac{5}{4}$
$\Rightarrow 4(4x + 2) = 5(3x + 2)$
$\Rightarrow x = 2$
Sum of their present ages $= (4x + 1 + 3x + 1)$$=(7x + 2) = 16$ years

12. The ratio between the ages of A and B at present is 2:3. Five years hence the ratio of their ages will be 3:4. What is the present age of A ?
a. 10 years
b. 15 years
c. 25 years
d. Data inadequate

Answer: A
Explanation:
Let the ages of A and B be = $2x, \;3x$ years.
$\begin{array}{*{20}{|c|cc|}} \hline
{}&{A}&{B} \\ \hline
\text{Present ages}&{2x}&{3x} \\ \hline
\text{5 years hence ages}&{2x+5}&{3x+5} \\ \hline
\end{array}$
$\displaystyle\frac{{2x + 5}}{{3x + 5}} = \displaystyle\frac{3}{4}$
$\Rightarrow 4(2x + 5) = 3(3x + 5)$
$\Rightarrow x = 5$
A's present age $= 2x = 10$ years

13. The ratio of the ages of father and son 10 years ago is 7:1. 5 years hence the ratio of their ages will become 5:2. The present age of the son is :
a. 5 years
b. 6 years
c. 9 years
d. 10 years

Answer: A
Explanation:
Let the ages of father and son 10 years ago $= 7x,\;x$ years
$\begin{array}{*{20}{|c|cc|}} \hline
{}&{Father}&{Son} \\ \hline
\text{10 yeas ago ages}&{7x}&{x} \\ \hline
\text{Present ages}&{7x+10}&{x+10} \\ \hline
\text{5 years hence ages}&{7x+15}&{x+15} \\ \hline
\end{array}$
$\displaystyle\frac{{7x + 15}}{{x + 15}} = \displaystyle\frac{5}{2}$
$\Rightarrow 2(7x + 15) = 5(x + 15)$
$\Rightarrow 14x + 30 = 5x + 75$
$\Rightarrow 9x = 45$
$\Rightarrow x = 5$
Son's present age $= x + 10 = 15$ years

14. Ratio of Ashok's age to Pradeep's age is equal to 4:3 Ashok will be 26 years old after 6 years. How old is Pradeep now ?
a. 12 years
b. 15 years
c. $19\displaystyle\frac{1}{2}$ years
d. 21 years

Answer: B
Explanation:
Ashok's present age $=26 - 6 = 20$ years
Let Ashok's age = $4x$ and Pradeep's age = $3x$ years
$ \Rightarrow 4x = 20 $
$\Rightarrow x = 5$
Pradeep's age = $3x = 3 \times 5 = 15$ years

15. Kamala got married 6 years ago. Today her age is $1\displaystyle\frac{1}{4}$ times her age at the time of marriage. Her son's age is $\left( {\displaystyle\frac{1}{{10}}} \right)$ times her age. Her son's age is :
a. 2 years
b. 3 years
c. 4 years
d. 5 years

Answer: B
Explanation:
Let Kamala's age 6 years ago be $x$ years, then Kamala's present age = $x+6$ years
$ \Rightarrow $ $(x + 6) = \displaystyle\frac{5}{4}x$
$ \Rightarrow $ $4x+24 = 5x$
$ \Rightarrow $ $x = 24$
So Kamala's present age = 30 years, Son's present age = $\left( {\displaystyle\frac{1}{{10}} \times 30} \right) = 3$ years

16. 10 years ago, Chandravati's mother was 4 times older than her daughter. 10 years hence, the mother will be twice older than the daughter. The present age of Chandravati is:
a. 5 years
b. 10 years
c. 20 years
d. 30 years

Answer: C
Explanation:
Let Chandravati's age 10 years ago be $x$ years.
Chandravati's age 10 years hence = $x + 20$ years.
Mother's age 10 years ago = $4x$ years
Mother's age 10 years hence = $4x + 20$ years
$\begin{array}{*{20}{|c|c|c|}} \hline
{}&{Mother}&{Chandravati} \\ \hline
\text{10 years ago ages}&{4x}&{x} \\ \hline
\text{Present ages}&{4x+10}&{x+10} \\ \hline
\text{10 years later ages}&{4x+20}&{x+20} \\ \hline
\end{array}$
$ \Rightarrow \dfrac{{4x + 20}}{{x + 20}} = \dfrac{2}{1}$
$ \Rightarrow $ $2(x + 20)=(4x + 20)$
$\Rightarrow x = 10$
Present age of Chandravathi = $(x + 10)=20$ years

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