A, B and C working together can do a piece of work in 8 hours. A alone

1.	A, B and C working together can do a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?1. 30 hours2. 32 days3. 34 hours4. 35 hours5. 40 hours
Answer» Correct Answer - Option 1 : 30 hours Given: A can do a piece of work in 20 hours B can do same work in = 24 hours A, B, and C working together can do the same work in = 8 hours Concept Used: If a man can do a work in x hours then he will do 1/x part of the work in 1 hour. Calculation: Work done by A in 1 hour = 1/20 Work done in 1 hour = 1/24 hour Work done by A, B, C together in 1 hour =18 We know that, Work done by C in 1 hour = work done A, B, and C in 1 hour-work done by A and B in 1 hour ⇒ \(\frac{1}{8} - \left( {\frac{1}{{20}} + \frac{1}{{24}}} \right)\) ⇒ \(\frac{1}{8} - \frac{{11}}{{120}}\) ⇒ (15 - 11)/120 (by taking LCM for 8and 120 which is 120 ⇒ \(\frac{4}{{120}}\) ⇒ 1/30 ∴ C complete the work is 30 hours

A, B and C working together can do a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?1. 30 hours2. 32 days3. 34 hours4. 35 hours5. 40 hours

Answer» Correct Answer - Option 1 : 30 hours

Given:

A can do a piece of work in 20 hours

B can do same work in = 24 hours

A, B, and C working together can do the same work in = 8 hours

Concept Used:

If a man can do a work in x hours then he will do 1/x part of the work in 1 hour.

Calculation:

Work done by A in 1 hour = 1/20

Work done in 1 hour = 1/24 hour

Work done by A, B, C together in 1 hour =18

We know that,

Work done by C in 1 hour = work done A, B, and C in 1 hour-work done by A and B in 1 hour

⇒ \(\frac{1}{8} - \left( {\frac{1}{{20}} + \frac{1}{{24}}} \right)\)

⇒ \(\frac{1}{8} - \frac{{11}}{{120}}\)

⇒ (15 - 11)/120 (by taking LCM for 8and 120 which is 120

⇒ \(\frac{4}{{120}}\)

⇒ 1/30

∴ C complete the work is 30 hours