Question
Manoj can complete a job in 10 days which Rakesh can do
in 15 days. Rakesh can finish a task in 20 days which Suresh can complete in 25 days. In how many days Suresh and Rakesh together can finish the work that Manoj can do in 90 days?Solution
Let the efficiency of Manoj, Rakesh, and Suresh be p, q, and r units/day respectively. So, 10p = 15q p = 15q / 10 p = 3q / 2 Again, 20q = 25r r = 20q / 25 r = 4q / 5 Now, ratio of efficiencies of Manoj, Rakesh, and Suresh = (3q/2) : q : (4q/5) Multiply each term by 10 to remove fractions = (15q) : (10q) : (8q) ⇒ 15 : 10 : 8 Let p = 15e, q = 10e, and r = 8e Let required time = T days So, (10e + 8e) × T = 15e × 90 ⇒ 18T = 1350 ⇒ T = 75 days
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