Question

X can complete a task in 15 days, and Y can complete the same task in 20 days. If X and Y work on alternate days starting with X, in how many days will the work be completed?

• A. 17
• B. 22
• C. 15
• D. 19

Answer 1

Answer:

A. 17

We are given:

• X’s 1-day work = ( \frac{1}{15} )

• Y’s 1-day work = ( \frac{1}{20} )

• They work alternately starting with X

  Work in 2 days (X + Y)

$\frac{1}{15} + \frac{1}{20}$

LCM = 60:

$= \frac{4}{60} + \frac{3}{60} = \frac{7}{60}$

So in 2 days → work done = 7/60

Find full cycles needed

We need 1 full work:

After 8 such cycles (16 days):
$8 \times \frac{7}{60} = \frac{56}{60} = \frac{14}{15}$

Remaining work:
$1 - \frac{14}{15} = \frac{1}{15}$

Next day is X’s turn

X does:
$\frac{1}{15}$

So remaining work completes exactly in next day

Total days

• 16 days + 1 day = 17 days

  Final Answer: 17 days