CSAT: Work Efficiency Quiz

Question

Surya can complete a work in 24 days and Ananya can complete the same work in 36 days. They work together for 8 days. After that, Ananya leaves and Surya’s efficiency increases by 50%. In how many total days will the entire work be completed?

Accepted Answer

Surya can complete the work in 24 days, so his one-day work is 1/24. Ananya can complete the work in 36 days, so her one-day work is 1/36. Step 1: Work done together in 8 days First, find their combined one-day work: 1/24 + 1/36 The LCM of 24 and 36 is 72. 1/24 = 3/72 1/36 = 2/72 So together, they complete 5/72 of the work per day. In 8 days, the work completed is: 8 × 5/72 = 40/72 = 5/9 So, 5/9 of the work is completed, and the remaining work is: 1 − 5/9 = 4/9 Step 2: Surya’s efficiency increases by 50% Original rate = 1/24 If efficiency increases by 50%, the new rate becomes: 1/24 × 1.5 = 1/16 So now Surya can complete the work alone in 16 days. Step 3: Time to complete remaining work Remaining work = 4/9 Surya’s new one-day work = 1/16 Time required: (4/9) ÷ (1/16) = (4/9) × 16 = 64/9 ≈ 7.11 days Step 4: Total time taken They worked together for 8 days, then Surya worked alone for about 7.11 days. Total time = 8 + 64/9 = 136/9 ≈ 15.11 days The closest option given is: 16 days (Option B)

Answer

14 days

Answer

16 days

Answer

18 days

Answer

20 days

Options

Explanation

Given

Solution

Step 1: Daily work rates

Step 2: Combined 1-day work

Step 3: Work done in 8 days

Step 4: Surya’s new efficiency

Step 5: Time to complete remaining work

Step 6: Total time

✅ Answer

Question