Quant Quiz

Problems on Age - Solved Examples (Set 6)

26. The product of the ages of Syam and Sunil is $240$. If twice the age of Sunil is more than Syam's age by $4$ years, what is Sunil's age?
A. $16$	B. $14$
C. $12$	D. $10$

answer with explanation

Answer: Option C
Explanation:
Let age of Sunil $=x$ and
age of Syam $=y$

$xy=240\cdots \left(1\right)$

$2x=y+4\Rightarrow y=2x-4\Rightarrow y=2(x-2)\cdots \left(2\right)$

Substituting equation $\left(2\right)$ in equation $\left(1\right)$. We get
$x\times 2(x-2)=240\Rightarrow x(x-2)=\frac{240}{2}\Rightarrow x(x-2)=120\cdots \left(3\right)$

We got a quadratic equation to solve.

Always time is precious and objective tests measure not only how accurate you are but also how fast you are. We can solve this quadratic equation in the traditional way. But it is more easy to substitute the values given in the choices in the quadratic equation (equation $3$) and see which choice satisfy the equation.

Here, option A is $10$. If we substitute that value in the quadratic equation, $x(x-2)=10\times 8$ which is not equal to $120$

Now try option B which is $12$. If we substitute that value in the quadratic equation, $x(x-2)=12\times 10=120$. See, we got that $x=12$

Hence Sunil's age $=12$

(Or else, we can solve the quadratic equation by factorization as,
$x(x-2)=120\Rightarrow x^2-2x-120=0\Rightarrow (x-12)(x+10)=0\Rightarrow x=12\text{or}-10$
Since $x$ is age and cannot be negative, $x=12$

Or by using quadratic formula as
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{2\pm \sqrt{(-2{)}^2-4\times 1\times (-120)}}{2\times 1}=\frac{2\pm \sqrt{4+480}}{2}=\frac{2\pm \sqrt{484}}{2}=\frac{2\pm 22}{2}=12\text{or}-10$

Since age is positive, $x=12$

27. One year ago, the ratio of Sooraj's and Vimal's age was $6:7$ respectively. Four years hence, this ratio would become $7:8$. How old is Vimal?
A. $32$	B. $34$
C. $36$	D. $38$

answer with explanation

Answer: Option C
Explanation:
Let the age of Sooraj and Vimal, $1$ year ago, be $6x$ and $7x$ respectively.

Given that, four years hence, this ratio would become $7:8$
$\Rightarrow (6x+5):(7x+5)=7:8\Rightarrow 8(6x+5)=7(7x+5)\Rightarrow 48x+40=49x+35\Rightarrow x=5$

Vimal's present age
$=7x+1=7\times 5+1=36$

28. The total age of A and B is $12$ years more than the total age of B and C. C is how many year younger than A?
A. $10$	B. $11$
C. $12$	D. $13$

answer with explanation

Answer: Option C
Explanation:
Solution 1

Given that, A + B $=12+$ B + C
⇒ A - C $=12$
Therefore, C is younger than A by $12$ years

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Solution 2

Total age of A and B is $12$ years more than total age of B and C.

Since B is common in both sides, C is $12$ years younger than A.

29. Sachin's age after $15$ years will be $5$ times his age $5$ years back. Find out the present age of Sachin?
A. $10$ years	B. $11$ years
C. $12$ years	D. $13$ years

answer with explanation

Answer: Option A
Explanation:
Let present age of Sachin $=x.$ Then,

$(x+15)=5(x-5)\Rightarrow 4x=40\Rightarrow x=10$

30. Sandeep's age after six years will be three-seventh of his father's age. Ten years ago the ratio of their ages was $1:5$. What is Sandeep's father's age at present?
A. $30$ years	B. $40$ years
C. $50$ years	D. $60$ years

answer with explanation

Answer: Option C
Explanation:
Let the age of Sandeep and his father before $10$ years be $x$ and $5x$ respectively.

Given that Sandeep's age after six years will be three-seventh of his father's age
$\Rightarrow x+16=\frac{3}{7}(5x+16)\Rightarrow 7x+112=15x+48\Rightarrow 8x=64\Rightarrow x=8$

Sandeep's father's present age
$=5x+10=5\times 8+10=50$