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A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for ₹ ₹3,200. With the help of C, they completed the work i
Question

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for ₹ ₹3,200. With the help of C, they completed the work in 3 days. How much is to be paid to B?

A.

₹ 800

B.

₹ 1,200

C.

₹ 1,400

D.

₹ 600

Correct option is B

Given:

A alone can do a piece of work in 6 days.

B alone can do the same work in 8 days.

A and B, with the help of C, completed the work in 3 days.

The total payment for the work is ₹ 3,200. 

Solution

Total work LCM of 6 , 8 and 3 = 24  

Efficiency of A = 246=4\frac{24}{6} = 4  

Efficiency of B = 248=3\frac{24}{8} = 3 ​​

Efficiency of A + B +  C = 243=8\frac{24}{3} = 8

Efficiency  of C = 8 - ( 4 + 3) = 1 

Work done by A in 3 days = 4×3\times 3  = 12

Work done by B in 3 days = 3×3=93\times 3 = 9  

Work done by C in 3 days = 3×13 \times 1 = 3

Work is proportional to wages, 

Wages ratio  = 12    :   9    :   3  

= 4     :    3   :  1  

(4 + 3 + 1) unit = 3200 

1 unit = 400

Then B wages = 3×400\times 400  = 1200 ​

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