(solved)Question 4 SSC-CGL 2018 June 4 Shift 1

Solution by Clever Trick

Four years ago, sum of their ages are $\displaystyle 4k + 5k = 9k$.

Hence, the sum of ages four years back has to be a multiple of $\displaystyle 9$.

Check first option: sum 4 years back is 76 - 8 = 68, not a multiple of 9. Rejected.

Check second option: sum 4 years back is 72 - 8 = 64, not a multiple of 9. Rejected.

Check third option: sum 4 years back is 80 - 8 = 72. Possible.

Similarly, fourth option also impossible.

Hence the answer is $\displaystyle 80$

Solution by Fundamentals

Use this fact: the difference of the ages of two persons always remains same. For example, if you are two years elder to your sister, then you will always remain two years elder.

The difference in ages of A and B as per the ratio 11 : 13 is 2 [i.e., 13 - 11].

Now rewrite the ratio 4 : 5 as 8 : 10 so that the difference is 2 for this ratio also.

Unitary method: If increase in age of A is (11 - 8) = 3, then his age four years back was 8.

If the increase in age of A is 12 [4 years back + 8 years later], then the age four years back should be $\displaystyle \frac{8}{3} \times 12 = 32$

Similarly, age of B four years back should be $\displaystyle 40$

Sum of present ages = $\displaystyle (40 + 4) + (32 + 4) = 80$ years Ans.

Solution by another Clever Trick

From the ratio of their ages four years ago, we can infer that their present ages are $\displaystyle 4k + 4$ and $\displaystyle 5k + 4$

Sum of ages is $\displaystyle 9k + 8$, where $\displaystyle k$ IS A NATURAL WHOLE NUMBER.

Check the first option [i.e., 76]. The sum of ages as $\displaystyle 9k + 8 = 76$ gives $\displaystyle k = 68/9$ which contradicts the fact that $\displaystyle k$ should be a whole number. This option is rejected.

Check second option, $\displaystyle 9k + 8 = 72$ is possible for $\displaystyle k = 7$.

But then their present ages will be $\displaystyle 4 k + 4 \equiv 32$ and $\displaystyle 5 k + 4 \equiv 39$

Ratio $\displaystyle 8$ years later will be $\displaystyle \frac{32 + 8}{39 + 8} \ne \frac{11}{13}$

Hence second option is not possible.

Check third option, $\displaystyle 9k + 8 = 80$ is possible for $\displaystyle k = 8$.

Present ages will be $\displaystyle 36$ and $\displaystyle 44$

Ratio $\displaystyle 8$ years later will be $\displaystyle \frac{36 + 8}{44 + 8} = \frac{11}{13}$

Hence third option is correct. On similar lines, we can verify that fourth is not possible.