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A works twice as fast as B and B works twice as fast as C. All three working together can finish a task in 4 days with the help of D. If D
alone can finish the same task in 16 days, then in how many days will A alone finish 75% of the same task?
8
7
9
6
Let’s break it down:
- A works twice as fast as B, and B works twice as fast as C.
- So, if C does 1 unit/day, B does 2 units/day, and A does 4 units/day.
- Together, A+B+C = 4+2+1 = 7 units/day.
- D alone finishes the job in 16 days, so D does 1/16 of the work per day.
- All four together finish in 4 days.
- So, (A+B+C+D) × 4 = 1 whole job.
- That’s (7 + 1/16) × 4 = 1.
- Let’s calculate:
- 7 + 1/16 = 113/16 units/day.
- In 4 days: (113/16) × 4 = 113/4 units.
- This much work must equal the whole job (which is 1), but the calculation shows that actually (A+B+C+D) = 1/4 units/day.
- Actually, (A+B+C+D) × 4 = 1
So (A+B+C+D) = 1/4 per day.
- We already have D = 1/16 per day.
- So, (A+B+C) = 1/4 – 1/16 = (4-1)/16 = 3/16 per day.
- A+B+C = 3/16 per day.
We also know A:B:C = 4:2:1, so total shares = 7.
So A = 4/7 × (3/16) = 12/112 = 3/28 per day.
- To finish 75% of the job:
- Time = (3/4)/(3/28) = (3/4) × (28/3) = 28/4 = 7 days.
Here’s what’s up with the options:
- 1, 8 – Nope
- 2, 7 – Yes, that’s exactly what we calculated
- 3, 9 – No
- 4, 6 – No
By: santosh ProfileResourcesReport error
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