35 men can do a piece of work in 8 days. Find the time required by 16 men to do four times the work.

Correct — A. Measure the job in man-days (men × days).

One work: 35 men × 8 days = 280 man-days
Four times the work: 280 × 4 = 1,120 man-days
Divide by the new crew: 1,120 ÷ 16 = 70 days → option (a)

The same in one line: D₂ = M₁ × D₁ × 4 ⁄ M₂ = 35 × 8 × 4 ⁄ 16 = 70.

Why the others are wrong

• (b)
  65 Days — 16 men × 65 days = 1,040 man-days, which is 80 short of the 1,120 man-days that four times the work needs.
• (c)
  60 Days — 16 × 60 = 960 man-days, enough for only 960 ÷ 280 ≈ 3.4 times the original work, not 4.
• (d)
  66 Days — 16 × 66 = 1,056 man-days, still 64 short of 1,120, so the job would be left unfinished.

When every worker has the same daily rate, the effort a job needs is men × days, counted in man-days.

That effort scales with the amount of work: four times the work needs four times the man-days. Spreading it over fewer men stretches the days in proportion.

The combined rule is M₁D₁ ⁄ W₁ = M₂D₂ ⁄ W₂, with W the amount of work. When hours per day are given, include them: M₁D₁H₁ ⁄ W₁ = M₂D₂H₂ ⁄ W₂.

Key facts

• Man-days = workers × days, assuming every worker has the same rate.
• Days vary inversely with the number of workers and directly with the amount of work.
• M₁D₁ ⁄ W₁ = M₂D₂ ⁄ W₂ links two crews doing different amounts of work.

Common traps

• Scaling by 16 ⁄ 35 instead of 35 ⁄ 16: fewer men must take more days, not fewer.
• Dropping the ×4: 280 ÷ 16 = 17.5 days is the time for the original job, not four times it.

No directly related past PYQ was found.