SSC GD 2024 PYQ — Question 59

The correct answer is option 4 i.e. 360/11 days.

Given that

Rakhi completes 10 percent of the work in = 8 days

The efficiency of Poonam = 20 percent more than Rakhi = $\frac{120}{100}$ of Rakhi

Let the total work be denoted by = W

Let the efficiency of Rakhi be = R

Hence, the efficiency of Poonam is = 1.2R

According to the question

Rakhi works for 8 days with efficiency R and completes 10 percent of W

⇒ 8R = 0.1W

Now, when both of them work together the efficiency becomes = R + 1.2R = 2.2R

Let them work together for N days

⇒ (2.2R)A = 0.9W

Dividing both equations we get the value of A = $\frac{8 × 0.9}{2.2 × 0.1}$ = $\frac{7.2}{0.22}$

Now, $\frac{7.2}{0.22}$ = $\frac{360}{11}$ = 32.72

Hence, they both complete the remaining work in $\frac{360}{11}$ days.