The efficiency of C is 20% more than the efficiency of D. D alone can complete a piece of work in (y-2) days. The time taken by C alone to complete the work is 11 days less than the time taken by E alone to complete the same work. If the ratio between the efficiency of D and E is 6:5 respectively, then find out the value of ‘y’.

Solution

If the ratio between the efficiency of D and E is 6:5 respectively. Let’s assume the efficiency of D and E is ‘6a‘ and ‘5a’ respectively. The efficiency of C is 20% more than the efficiency of D. efficiency of C = (100+20)% of 6a = 120% of 6a = 7.2a D alone can complete a piece of work in (y-2) days. Total work = 6a(y-2) The time taken by C alone to complete the work is 11 days less than the time taken by E alone to complete the same work. [6a(y-2)]/7.2a = [6a(y-2)/5a]-11 [(y-2)]/1.2 = [1.2(y-2)]-11 (y-2) = 1.44(y-2)-13.2 13.2 = 1.44(y-2)-(y-2) (y-2)[1.44-1] = 13.2 0.44(y-2) = 13.2 (y-2) = 30 Value of ‘y’ = 30+2 = 32