A and B together can do a piece of work in (p-8.8) days.The efficiency of D is 10% less than the efficiency of B. A and C together can do the same piece of work in (p-8) days. D alone can do the same piece of work in 20 days. The ratio between the efficiencies of B and C is 4:3 respectively. Find out the value of ‘p’.

Solution

Let’s assume the total work is 360 units. D alone can do the same piece of work in 20 days. Efficiency of D = 360/20 = 18 units/day The efficiency of D is 10% less than the efficiency of B. 18 = (100-10)% of efficiency of B 18 = 90% of efficiency of B 18 = 0.9 x (efficiency of B) efficiency of B = 20 units/day The ratio between the efficiencies of B and C is 4:3 respectively. efficiency of C = (20/4)x3 = 15 units/day A and B together can do a piece of work in (p-8.8) days. (Efficiency of A + 20) x (p-8.8) = 360 (Efficiency of A + 20) = 360/(p-8.8) Efficiency of A = [360/(p-8.8)] - 20    Eq.(i) A and C together can do the same piece of work in (p-8) days. (Efficiency of A + 15) x (p-8) = 360 (Efficiency of A + 15) = 360/(p-8) Efficiency of A = [360/(p-8)] - 15    Eq.(ii) So Eq.(i) = Eq.(ii) [360/(p-8.8)] - 20 = [360/(p-8)] - 15 [360/(p-8.8)] - [360/(p-8)] = 20-15 [360/(p-8.8)] - [360/(p-8)] = 5 [72/(p-8.8)] - [72/(p-8)] = 1 5p ² -84p+64 = 0 5p ² -(80+4)p+64 = 0 5p ² -80p-4p+64 = 0 5p(p-16)-4(p-16) = 0 (p-16) (5p-4) = 0 p = 16, 0.8 Here the value of ‘p’ will not be 0.8. Because some of the values will be negative which is not possible. So the value of ‘p’ = 16