Question

A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

• A. 12 days
• B. 15 days
• C. 16 days
• D. 18 days

Hint:

When helpers join periodically (e.g., “every third day”), compute the work per cycle and multiply—this avoids fractional end-days and makes checking easy.

Answer 1

The Correct Option is B

Step 1 (Convert times to daily rates).
Let the total work be \(1\). Then rates are \(A=\frac{1}{20},\ B=\frac{1}{30},\ C=\frac{1}{60}\) (work/day).
Step 2 (Compute LCM to combine easily).
LCM of \(20,30,60\) is \(60\). In “sixtieths of work”: \(A=3/60,\ B=2/60,\ C=1/60.\)
Step 3 (Model the 3-day cycle).
Day 1: A alone \(=3/60\).
Day 2: A alone \(=3/60\).
Day 3: A + B + C \(=(3+2+(a)/60=6/60=1/10.\)
Total work in 3 days \(=\frac{3}{60}+\frac{3}{60}+\frac{6}{60}=\frac{12}{60}=\frac{1}{5}.\)
Step 4 (Scale cycles to finish full work).
Each 3-day block completes \(\frac{1}{5}\) of the job \(\) need \(5\) such blocks.
Total time \(= 5 \times 3 = 15\) days.
Step 5 (Sanity check—no leftover).
\(5 \times \frac{1}{5} = 1\) exactly, so the job ends at the close of a full 3-day cycle. \[ \boxed{15 \ \text{days (Option (b)}} \]