Question
Aman' and 'Bhuvan' can complete a
certain task in 24 days and 40 days, respectively. Both started working together, but 'Bhuvan' left after 5 days. Afterward, 'Aman' continued working alone until 'Chintu' joined him, and together they completed the task in an additional 5 days. If, instead of 'Chintu,' 'Bhuvan' had rejoined 'Aman' during this second phase of work, it would have taken them 37.5% longer to complete that phase compared to the time taken by 'Aman' and 'Chintu' working together. Quantity-I: Calculate the time 'Chintu' would take to complete the work alone. Quantity-II: Determine the total duration 'Aman' worked. In the question, two Quantities I and II are given. You have to solve both the Quantity to establish the correct relation between Quantity-I and Quantity-II and choose the correct option.Solution
ATQ, Let the total work be 120 units. {LCM (24 and 40) } So, efficiency of 'Aman' = (120/24) = 5 units/day And efficiency of 'Bhuvan' = (120/40) = 3 units/day Let the efficiency of 'Chintu' be 'p' units/day ATQ: (5 + p) × 5 = (5 + 3) × (5 × 1.375) Or, (5 + p) = 8 × 1.375 Or, 5 + p = 11 So, 'p' = 6 Also, efficiency of 'Chintu' = 6 units/day Quantity I: Time taken by 'Chintu' to finish the work alone = (120/6) = 20 days So, Quantity I = 20 days Quantity II: Work done by 'Aman' and 'Bhuvan' in first five days = 5 × (5 + 3) = 40 units And work done by 'Aman' and 'Chintu' in last 5 days = 5 × (5 + 6) = 55 units And work done by 'Aman' alone = 120 - (55 + 40) = 25 units So, 'Aman' worked alone for 25 ÷ 5 = 5 days So, 'Aman' worked for a total of (5 + 5 + 5) = 15 days So, Quantity II = 15 days So, Quantity I > Quantity II
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