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17 men can dig a ditch 26 m long in 18 days, working 8 hours a day. How many more men should be engaged to dig a similar ditch 39 m long in 6 days, each man now working 9 hours a day?
48
55
51
53
51
This quantitative aptitude question uses the Chain Rule / Work-Equivalence formula: (M1 × D1 × H1) / W1 = (M2 × D2 × H2) / W2. Plugging in the values: (17 × 18 × 8) / 26 = (M2 × 6 × 9) / 39, which simplifies to M2 = 68 men. The total men required is 68, meaning 68 - 17 = 51 additional men must be engaged.
This quantitative aptitude question uses the Chain Rule / Work-Equivalence formula: (M1 × D1 × H1) / W1 = (M2 × D2 × H2) / W2. Plugging in the values: (17 × 18 × 8) / 26 = (M2 × 6 × 9) / 39, which simplifies to M2 = 68 men. The total men required is 68, meaning 68 - 17 = 51 additional men must be engaged.
Chain Rule and Unitary Method principles form the core foundational arithmetic taught in standard Indian secondary school curricula (NCERT) and are heavily tested across SSC, Banking, and Railway exams.
Work Equivalence Formula: (M1 × D1 × H1) / W1 = (M2 × D2 × H2) / W2
Substituting given values: (17 × 18 × 8) / 26 = (M2 × 6 × 9) / 39
Solving for total men (M2) gives 68 men.
Subtracting initial men: 68 - 17 = 51 additional men required.
Total work rate required is directly proportional to the length of the ditch and inversely proportional to available days and daily working hours.
Initial manpower M1 = 17, total new required workforce M2 = 68.
Option A (48), Option B (55), and Option D (53) are incorrect calculation traps resulting from miscalculating total workforce or failing to subtract the initial 17 men.
C is correct — Solving the work-equivalence equation gives M2 = 68 total men, requiring 51 more men to be engaged.
Time and Work problems using the compound proportion rule (M1 D1 H1 / W1 = M2 D2 H2 / W2) frequently appear alongside Pipe and Cistern problems in competitive exams like SSC and Railways.
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