Three men can do as much work as 5 boys; and the wages of 3 boys are equal to those of 2 men. A work on which 40 boys and 15 men are employed takes 8 weeks and costs Rs.15750. How long would it take if 20 boys and 20 men were employed, and how much would it cost?
Solution
Correct Answer: Option B
Let the work of men be M and work of boys be B and their wages be wm and wb
Given 3 men can do as much work as 5 boys and wage of 2 men is equal to wage of 3 boys
∴ 3M = 5B
⇒ M = 5B/3
And 2wm= 3wb
⇒ wm= 3wb/2
40 boys and 15 men work for 8 weeks to complete a job and the work costs 15750
Total work done = 40B + 15M
⇒ Total work done = 40B + 15 × 5B/3
⇒ Total work done = 65B
Thus to complete 65B work 8 weeks are required
Total wage = 40wb+ 15wm
⇒ Total wage = 40wb+ 45wb/2 = 125wb/2
Given Total cost of work = 15750
Total cost = wage × number of weeks
15750 = 125wb/2 × 8
⇒ wb= 31.5
If 20 men and 20 boys work then
Total work = 20M + 20B
⇒ Total work = 20 × 5B/3 + 20B
⇒ Total work = 160B/3
To complete 65B work it took 8 weeks
∴ To complete 160B/3 time taken = \(\frac{8}{{\frac{{160B}}{3}}} \times 65B\)
⇒ Time taken to complete 160B/3 work = 39/4 = 9 ¾ Weeks
Total wage = 20wm+ 20wb
⇒ Total wage = 30wb+ 20wb= 50wb
Total cost = wage × number of weeks
⇒ Total cost = 50 × 31.5 × 39/4
⇒ Total cost = 15356.25
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