Question

Deep and john can do a piece of work in 12 days while John and Titu can do the same work in 16 days. Deep starts the work for 5 days. He is then replaced by john who works for 7 days. Titu is finishing the remaining work in 13 days. If at the end of the work they get Rs.9600 john’s share in it is:

Answer 1

Answer: Rs. 1600

Explanation:

Deep and John can do the work in 12 days

John and Titu can do the work in 16 days

∴ Work done by (Deep + John) in 1 day = 1/12 ….. (i)

∴ Work done by (John + Titu) in 1 day = 1/16 ….. (ii)

Step 1:

Let work done by Titu in 1 day be “x”.

According to the question,

(Work done by Deep in 5 days) + (Work done by John in 7 days) + (Work done by Titu in 13 days) = 1

⇒ (Work done by Deep & John in 5 days) + (Work done by John & Titu in 2 days) + (Work done by Titu in 11 days) = 1

⇒ 5/12 + 2/16 + 11x = 1

⇒ 5/12 + 1/8 + 11x = 1

⇒ 13/24 + 11x = 1

⇒ 11 x = 11/24

⇒ x = 1/24 ← Titu’s 1 day work ….. (iii)

Step 2:

Subtracting (iii) from (ii), we get

John’s 1 day work = 1/16 – 1/24 = 1/48 ….. (iv)

And,

Subtracting (iv) from (i), we get

Deep’s 1-day work = 1/12 – 1/48 = 3/48 = 1/16 ….. (v)

Step 3:

At the end of their work they get Rs. 9600.

From (iii), (iv) & (v), we get

The ratio of their share as,

Deep : John : Titu  

= $\frac{1}{16}$  : $\frac{1}{48}$ : $\frac{1}{24}$

Multiplying each ratio by L.C.M. of denominators = 48,

= 3 : 1 : 2

Thus,  

John’s share

= $\frac{1}{3+1+2}$ * 9600

= $\frac{1}{6}$ * 9600

= Rs. 1600