A can do a work in 4 days, B can do same work in 8 days, then the time taken by A and B to do the same work together is: Option 1: 8/3 days Option 2: 3/8 days Option 3: 9/4 days Option 4: 6 days

Answer: 8/3 days. Solution: When A can do work in 4 days, in 1 day A completes 1/4 of the work. When B can do work in 8 days, in 1 day B completes 1/8 of the work. A's rate = 1/4 work per day B's rate = 1/8 work per day When A and B work together, their rates are added: Combined rate = 1/4 + 1/8 = 2/8 + 1/8 = 3/8 work per day Time = (Total Work)/(Rate) = 1/(3/8) = 1 x 8/3 = 8/3 days Therefore, A and B together complete the work in 8/3 days.

Arithmetic

Time & Work

Easy

A can do a work in 4 days, B can do same work in 8 days, then the time taken by A and B to do the same work together is:

8/3 days

3/8 days

9/4 days

6 days

✅ Correct Option: 1

When A can do work in 4 days, in 1 day A completes $\frac{1}{4}$ of the work.

When B can do work in 8 days, in 1 day B completes $\frac{1}{8}$ of the work.

A's rate $= \frac{1}{4}$ work per day

B's rate $= \frac{1}{8}$ work per day

When A and B work together, their rates are added:

Combined rate $= \frac{1}{4} + \frac{1}{8}$

$= \frac{2}{8} + \frac{1}{8}$

$= \frac{3}{8}$ work per day

Time $= \frac{\text{Total Work}}{\text{Rate}}$

$= \frac{1}{\frac{3}{8}}$

$= 1 \times \frac{8}{3}$

$= \frac{8}{3}$ days

Therefore, A and B together complete the work in $\frac{8}{3}$ days.

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Solution

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