A man completes 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work is further increased by 50% ?

Correct Option: (c) 18

A man completes 7/8 of a job in 21 days. First, let us find the total time required to complete the entire job (1 whole job). Time for the whole job = 21 × (8 / 7) = 3 * 8 = 24 days. Thus, the original job takes 24 days in total. Now, according to the problem, the quantum of work is further increased by 50%. The new total quantum of work becomes 1 + 50% of 1 = 1.5 times the original job. Therefore, the time required to complete this new increased quantum of work is 24 × 1.5 = 36 days. The man has already worked for 21 days. The question asks how *many more days* will it take him to finish the job. Remaining days = Total new days - Days already worked = 36 - 21 = 15 days? Wait, let's recalculate carefully. Total work is 1.5 times. 7/8 of work is done in 21 days. Remaining original work is 1/8, which takes 21 / 7 = 3 days. But work increases by 50% of total work. 50% of total work is half of 1 unit = 4/8 units. Total work to do now is 1 + 0.5 = 1.5 units. Work already done = 7/8 units. Remaining work = 1.5 - 7/8 = 12/8 - 7/8 = 5/8 units. Since 7/8 units take 21 days, 1/8 unit takes 3 days. Therefore, 5/8 units will take 5 × 3 = 15 days? Wait, let's recheck the options: (a) 24, (b) 21, (c) 18, (d) 15. Let's check UPSC official solution: Total time for 1.5 work is 36 days. Days already spent = 21. Additional days = 36 - 21 = 15? Wait, let's check: 7/8 of job in 21 days implies rate is (7/8)/21 = 1/24 per day. New work is 1.5 times = 3/2 of the job. Total days needed = (3/2) / (1/24) = (3/2) × 24 = 36 days. Remaining days = 36 - 21 = 15 days. Let's double check if option (d) is correct.