A and B can do a work in 21 days. A is 7/4 times as efficient as B. In how…
2020
A and B can do a work in 21 days. A is 7/4 times as efficient as B. In how many days, A alone can complete the 200/3% of the work?
- A.
36
- B.
33
- C.
22
- D.
27
Attempted by 4 students.
Show answer & explanation
Correct answer: C
Step 1 — Set up the efficiency ratio. A is 7/4 times as efficient as B, so efficiency of A : B = 7 : 4. Take A's rate = 7 units/day and B's rate = 4 units/day, giving a combined rate of 7 + 4 = 11 units/day.
Step 2 — Find the total work. A and B together finish the work in 21 days, so total work = combined rate × time = 11 × 21 = 231 units.
Step 3 — Time for A alone (full work). A does 7 units/day, so A alone needs 231 ÷ 7 = 33 days for the whole work.
Step 4 — Convert the required portion. 200/3% = (200/3) ÷ 100 = 2/3 of the work.
Step 5 — Time for A to do 2/3 of the work. Since A finishes the full work in 33 days, doing 2/3 of it takes (2/3) × 33 = 22 days.
Hence, A alone completes 200/3% of the work in 22 days.