Question
Asmita and Bhanu working together can complete the task
in ____ days, and the efficiency of Sam is 50% more than that of Asmita. Bhanu alone can complete one-fourth of the work in 15 days, and Sam alone can complete 60% of the work in ___ days. Which set of values from the following options will correctly fill the blanks in the given order to make the statement true: I. 48, 96 II. 40, 50 III. 30, 24Solution
ATQ, Time taken by ‘Bhanu’ alone to complete the work = 15 × 4 = 60 days Solving the question by options, For I: Time taken by ‘Asmita’ and ‘Bhanu’ together to complete the work = 48 days Let the total amount of the work = 240 units (LCM of 48 and 60) The efficiency of ‘Bhanu’ = 240/60 = 4 units/day The efficiency of ‘Asmita’ and ‘B’ together = 240/48 = 5 units/day The efficiency of ‘Asmita’ = 5 – 4 = 1 unit/day The efficiency of ‘Sam’ = 1 × 1.5 = 1.5 units/day Time taken by Sam to complete the work = 240/1.5 = 160 days Time taken by Sam to complete 60% of the work = 160 × 0.6 = 96 days Therefore, ‘I’ is true. For II: Time taken by ‘Asmita’ and ‘Bhanu’ together to complete the work = 40 days Let the total amount of the work = 120 units (LCM of 40 and 30) The efficiency of ‘Bhanu’ = 120/60 = 2 units/day The efficiency of ‘Asmita’ and ‘B’ together = 120/40 = 3 units/day The efficiency of ‘Asmita’ = 3 – 2 = 1 unit/day The efficiency of ‘Sam’ = 1 × 1.5 = 1.5 units/day Time taken by ‘Sam’ to complete the work = 120/1.5 = 80 days Time taken by ‘Sam’ to complete 60% of the work = 80 × 60% = 48 days Therefore, ‘II’ is false. For III: Time taken by ‘Asmita’ and ‘Bhanu’ together to complete the work = 30 days Let the total amount of the work = 60 units (LCM of 30 and 20) The efficiency of ‘Bhanu’ = 60/60 = 1 unit/day The efficiency of ‘Asmita’ and ‘B’ together = 60/30 = 2 units/day The efficiency of ‘Asmita’ = 2 – 1 = 1 unit/day The efficiency of ‘Sam’ = 1 × 1.5 = 1.5 units/day Time taken by ‘Sam’ to complete the work = 60/1.5 = 40 days Time taken by Sam to complete 60% of the work = 40 × 60% = 24 days Therefore, 'Ill' is true.
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