Question
A work is done by A, B, C and D together. The percentage
of work done by A, B C and D are in arithmetic progression (AP). The first, second, third and fourth term in the AP is the percentage of work done by A, B, C and D respectively. C works for nine days and complete (3/10)th the work and A and B worked for two days and three days only respectively and the remaining work is done by D. D alone can complete the total work in ‘m’ days and all four together can complete the whole work in four days. Total wages allotted for the work is Rs 45000 when they worked together to complete the work. The difference in the wages received by A and D is Rs. X. Find which of the statement is/are true. (I): Numerical value of X is the perfect cube (II): X (III): X is the product of the 1000 and the square of 3Solution
ATQ, Total wage = Rs 45000 Efficiency of A = (60/20) = 3 units/day Efficiency of B = (60/15) = 4 units/day Efficiency of C = 60/30=2 units/day Efficiency of D = (60/10) = 6 units/day Wage of A = (45000/15) × 3 = Rs.9000 Wage of D = (45000/15) × 6 = Rs.18000 Difference in the wage of A and D = 18000-9000 = Rs. 9000
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