Sameer can complete a work in 16 days. In how many days will the work be completed by Ajay, if his efficiency is 60% more than that of Sameer?

Correct — B. For the same work, time is inversely proportional to efficiency.

Sameer's efficiency = 100, so Ajay's = 100 + 60 = 160
Efficiency ratio Sameer : Ajay = 100 : 160 = 5 : 8
Time ratio is the reverse: 8 : 5

Ajay's time = 16 × 5⁄8 = 10 days → option (b)

Check in units: work = 16 × 5 = 80 units, Ajay does 8 a day, 80 ÷ 8 = 10.

Why the others are wrong

• (a)
  12 days — 12 days means Ajay works 16⁄12 = 4⁄3 as fast, only 33⅓% more efficient than Sameer, not 60%.
• (c)
  13 days — 13 days makes Ajay 16⁄13 ≈ 1.23 times as fast, about 23% more efficient. A 60% edge cuts the time further: 16 ÷ 1.6 = 10.
• (d)
  15 days — 15 days makes Ajay only 16⁄15 ≈ 1.07 times as fast, about 6.7% more efficient, far short of 60%.

For a fixed job, work = efficiency × time. Hold the work constant and efficiency and time move in opposite directions by the same factor.

60% more efficient means efficiency × 1.6, so time ÷ 1.6. It does not mean the time is cut by 60%.

16 ÷ 1.6 = 10 days, a 37.5% cut in time: 60 ÷ 160 = 0.375.

Key facts

• Work = efficiency × time
• For the same work, time is inversely proportional to efficiency
• If efficiency rises by r%, time falls by r ÷ (100 + r) × 100%: here 60 ÷ 160 = 37.5%

Common traps

• Cutting the time by 60% (16 × 0.4 = 6.4 days) instead of dividing it by 1.6
• Multiplying the time by 1.6 (25.6 days), as if more efficiency meant more days

No directly related past PYQ was found.