A can complete the work in 20 days. B can complete the same work in 30 days. A, B and C together completed the work in 7 days and received Rs.6000 as total wages. Find the share of C ?
Answers
Given:
A can complete the work in 20 days.
B can complete the same work in 30 days.
A, B, and C together completed the work in 7 days
They received Rs.6000 as total wages.
To find:
Find the share of C?
Solution:
Let, C can complete the work in x days.
A's 1 day work = 1/20
B's 1 day work = 1/30
C's 1 day work = 1/x
A, B, and C 1 day work = 1/20 + 1/30 + 1/x
= (3x + 2x + 60)/60x
= (5x + 60)/60x
= (x + 12)/12x
Days took to complete work by A, B, and C working together = 12x/(x + 12)
Since it is given that A, B, and C together completed the work in 7 days.
∴ 12x/(x + 12) = 7
12x = 7x + 84
12x - 7x = 84
5x = 84
x = 84/5 = 16⁴/₅
So, C can complete the work in 16⁴/₅ days.
∴ Share of C = 5/84 × 7 × 6000 = Rs. 2500
Therefore the share of C is Rs. 2500
Another method to solve the question:
A's 1 day work = 1/20
B's 1 day work = 1/30
Share of A = 1/20 × 7 × 6000 = Rs. 2100
Share of B = 1/30 × 7 × 6000 = Rs. 1400
∴ Share of C = 6000 - (Share of A + Share of B)
Share of C = 6000 - (2100 + 1400)
Share of C = 6000 - 3500
Share of C = Rs. 2500
Therefore the share of C is Rs. 2500