A can do a piece of work in 12 days while B alone can do it in 15 days. With the help of C they can finish it in 5 days. If they are paid Rs. 960 for the whole work how much money A gets?
A can do a piece of work in 12 days while B alone can do it in 15 days. With the help of C they can finish it in 5 days. If they are paid Rs. 960 for the whole work how much money A gets?
1). Rs. 480
2). Rs. 240
3). Rs. 320
4). Rs. 400
1 answers
Concept: $(\frac{1}{a}:\frac{1}{b}:\frac{1}{c} = \frac{{LCM\;of\;\left( {a,b,c} \right)}}{a}:\frac{{LCM\;of\;\left( {a,b,c} \right)}}{b}:\frac{{\left( {LCM\;of\;\left( {a,b,c} \right)} \right)}}{c})$
Given,
A can do a piece of work in 12 days.
∴ Part of work done by A in 1 day = 1/12
B can do a piece of work in 15 days
∴ Part of work done by B in 1 day = 1/15
Let,
C can do a piece of work in ‘x’ days
∴ Part of work done by C in 1 day = 1/x
? A, B and C can do the work in 5 days
$(\therefore \frac{1}{{12}} \times 5 + \frac{1}{{15}} \times 5 + \frac{1}{x} \times 5 = 1)$
$(\Rightarrow \frac{5}{{12}} + \frac{1}{3} + \frac{5}{x} = 1)$
⇒ (9/12) + (5/x) = 1
⇒ 5/x = 1 – (9/12)
⇒ 5/x = 3/12
⇒ x = 20
∴ Part of work done by C in 1 day = 1/20
∴ Ratio of part of work done by A, B and C
= 1/12 : 1/15 : 1/20
? LCM of 12, 15 and 20 is 60.
= (1/12) × 60 : (1/15) × 60 : (1/20) × 60
= 5 : 4 : 3
∴ Ratio of money A, B and C get
= 5 : 4 : 3
Given, Total money got by A, B and C together = Rs. 960
∴ Money A gets = {5/(5 + 4 + 3)} × 960 = (5/12) × 960 = Rs. 400