Subject
Quantitative Aptitude
Topic
Time and Work
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?
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?
ক)
6 weeks; Rs. 14356.75 pখ)
9 ¾ weeks; Rs. 15356.25 pগ)
12 weeks; Rs. 16365.25 pঘ)
15 weeks; Rs. 17345.75 pঙ)
None of theseExplanation
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 2w m = 3w b ⇒ w m = 3w b /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 = 40w b + 15w m ⇒ Total wage = 40w b + 45w b /2 = 125w b /2 Given Total cost of work = 15750 Total cost = wage × number of weeks 15750 = 125w b /2 × 8 ⇒ w b = 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 = ⇒ Time taken to complete 160B/3 work = 39/4 = 9 ¾ Weeks Total wage = 20w m + 20w b ⇒ Total wage = 30w b + 20w b = 50w b Total cost = wage × number of weeks ⇒ Total cost = 50 × 31.5 × 39/4 ⇒ Total cost = 15356.25Related questions
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