Question
- 3 men can do as much work as 5 boys. The wages of 3 boys are equal to those of 2 men. A piece of work for 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?
Answer: Option C
Let us assume that the efficiency of a man is 'm' and the efficiency of a boy is 'b'.Given,3m = 5b …… (1)3b wages = 2m wagesTherefore, b wages = (2/3)m wagesLet us assume that the total work is 'W' and the time taken to complete the work by 40 boys and 15 men is 'T' weeks.According to the question,40b + 15m = W …… (2)And, 40b wages + 15m wages = Rs 15750 …… (3)We can use equations (1), (2), and (3) to find the value of 'W'.40b + 15m = W40b + 15(m/2)(3/2) = W [Using equation (1)]40b + (45/4)b = W [Substituting m wages = (2/3)b wages]185b/4 = WNow, we can use the formula: Work = Efficiency × Time to find the time taken to complete the work with 20 boys and 20 men.20b + 20m = W …… (4)Let us assume that the time taken is 't' weeks.20b + 20(m/2)(3/2) = W [Using equation (1)]20b + (15/2)b = W [Substituting m wages = (2/3)b wages]35b/2 = WSince the amount of work done is the same in both cases, we can equate equations (2) and (4) to get:40b + 15m = 20b + 20m20b = 5m4b = mNow, we can use the formula: Work = Efficiency × Time to find the value of 't'.20b + 20m = W20b + 20(4b) = (185b/4)100b/4 = (185b/4) - 20b65b/4 = Wt = W / (20b + 20m)t = (65b/4) / (20b + 20(4b))t = (65/4) / (20 + 80)t = (65/4) / 100t = 13/80t = 0.1625 weeksNow, we can find the cost of the work with 20 boys and 20 men using the formula:Cost = Total Wages × Time × RateLet us assume that the rate is 'r' rupees per week per person.Total Wages for 20 boys and 20 men = 20b wages × 20 + 20m wages × 20 = (2/3)m wages × 20 × 20 + m wages × 20 × 20 = 800m wagesCost = 800m wages × 0.1625 weeks × rCost = 130m wages × rSubstituting the value of m wages in terms of b wages, we get:Cost = 130(3b/2) wages × rCost = 195brSubstituting the value of 'r' from equation (3), we get:Cost = 195br = 15750/8r = 15750/(8 × 195b)r = 4.054Now, we can find the cost of the work with 20 boys and 20 men using the formula:Cost = Total Wages × Time × RateTotal Wages forIf you think the solution is wrong then please provide your own solution below in the comments section .
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Let us assume that the efficiency of a man is 'm' and the efficiency of a boy is 'b'.Given,3m = 5b …… (1)3b wages = 2m wagesTherefore, b wages = (2/3)m wagesLet us assume that the total work is 'W' and the time taken to complete the work by 40 boys and 15 men is 'T' weeks.According to the question,40b + 15m = W …… (2)And, 40b wages + 15m wages = Rs 15750 …… (3)We can use equations (1), (2), and (3) to find the value of 'W'.40b + 15m = W40b + 15(m/2)(3/2) = W [Using equation (1)]40b + (45/4)b = W [Substituting m wages = (2/3)b wages]185b/4 = WNow, we can use the formula: Work = Efficiency × Time to find the time taken to complete the work with 20 boys and 20 men.20b + 20m = W …… (4)Let us assume that the time taken is 't' weeks.20b + 20(m/2)(3/2) = W [Using equation (1)]20b + (15/2)b = W [Substituting m wages = (2/3)b wages]35b/2 = WSince the amount of work done is the same in both cases, we can equate equations (2) and (4) to get:40b + 15m = 20b + 20m20b = 5m4b = mNow, we can use the formula: Work = Efficiency × Time to find the value of 't'.20b + 20m = W20b + 20(4b) = (185b/4)100b/4 = (185b/4) - 20b65b/4 = Wt = W / (20b + 20m)t = (65b/4) / (20b + 20(4b))t = (65/4) / (20 + 80)t = (65/4) / 100t = 13/80t = 0.1625 weeksNow, we can find the cost of the work with 20 boys and 20 men using the formula:Cost = Total Wages × Time × RateLet us assume that the rate is 'r' rupees per week per person.Total Wages for 20 boys and 20 men = 20b wages × 20 + 20m wages × 20 = (2/3)m wages × 20 × 20 + m wages × 20 × 20 = 800m wagesCost = 800m wages × 0.1625 weeks × rCost = 130m wages × rSubstituting the value of m wages in terms of b wages, we get:Cost = 130(3b/2) wages × rCost = 195brSubstituting the value of 'r' from equation (3), we get:Cost = 195br = 15750/8r = 15750/(8 × 195b)r = 4.054Now, we can find the cost of the work with 20 boys and 20 men using the formula:Cost = Total Wages × Time × RateTotal Wages forIf you think the solution is wrong then please provide your own solution below in the comments section .
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