Question

Two men undertake to do a piece of work for Rs. 5600. First man alone can do this work in 7 days while the second man alone can do this work in 8 days. If they work together and complete this work in 3 days with the help of a boy, then the amount the two men together get is (in rupees)
1. 4,000
2. 4,500
3. 4,580
4. 4,600

Answer 1

Correct Answer - Option 2 : 4,500

Given:

Two men get Rs. 5600 to complete the work.

First man can do a piece of work in 7 days

Second man can do a piece of work in 8 days

Two men and boy together can complete the work in 3 days

Calculation:

First man's 1 day's work = 1/7

Second man's 1 day's work = 1/8

Boy's 1 day's work = (1/3) - {(1/7) + (1/8)} = (1/3) - (15/56)

⇒ Boy's 1 day's work = (11/168)

⇒ Ratio of wages of the first man, second man and boy = (1/7) : (1/8) : (11/168)

L.C.M of 7, 8, 168 is 168

Ratio of wages of the first man, second man and boy = (1/7) × 168 : (1/8) × 168 : (11/168) × 168

⇒ Ratio of wages of the first man, second man and boy = 24 : 21 : 11

∴ Total share's the amount = 24 + 21 + 11 = 56 units 

⇒  First man's share = Rs. (24/56) × 5600 = Rs. 2400

⇒ Second man's share = Rs. (21/56) × 5600 = Rs. 2100

The amount shares in two men together get = 2400 + 2100 = 4500

∴  The amount the two men together get is Rs. 4500