Multiple choice

$36$ workmen are employed to finish a certain work in $48$ days but it is found that in $24$ days , only $\dfrac{2}{5}$ work is done. How many more men must be taken to finish the work in time?

  1. $16$
  2. $20$
  3. $18$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work done = 2/5 in 24 days by 36 men. Remaining work = 3/5. Remaining time = 48 - 24 = 24 days. Using M1D1/W1 = M2D2/W2: (36*24)/(2/5) = M2*24/(3/5). 36/(2/5) = M2/(3/5) => 36 * 5/2 = M2 * 5/3 => 18 * 3 = M2 => M2 = 54. Men to add = 54 - 36 = 18.

AI explanation

Using the formula M1 x D1 / W1 = M2 x D2 / W2, we have (36 x 24) / (2/5) = (M2 x 24) / (3/5). This equation shows that since the remaining work (3/5) is 1.5 times the completed work (2/5), you need 1.5 times the men. Solving gives M2 = 54 total men needed to finish the rest of the work in 24 days. Since 54 total men are needed and 36 men are already employed, 18 more men must be taken.

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