A can lay railway track between two specified stations in 16 days, while B can complete the same task in 12 days. When C assists them, they manage to finish the job in just 4 days. How long would it take for C to complete the job on their own?
- (a)8 1⁄2 days
- (b)9 1⁄2 days
- (c)9 3⁄5 days
- (d)10 days
Answer
Why
Correct — C. Take the total work as 48 units, the LCM of 16, 12 and 4.
A's rate: 48 ÷ 16 = 3 units a day
B's rate: 48 ÷ 12 = 4 units a day
A + B + C: 48 ÷ 4 = 12 units a day
C's rate = 12 − 3 − 4 = 5 units a day
C alone: 48 ÷ 5 = 9.6 days = 9 3⁄5 days → option (c)
Why the others are wrong
- (a)8 1⁄2 days — C would do 48 ÷ 8.5 ≈ 5.65 units a day, so the three together do 12.65 and finish in about 3.8 days, not 4.
- (b)9 1⁄2 days — Close, but 48 ÷ 5 = 9.6 days, and 0.6 of a day is 3⁄5, not 1⁄2. At 9½ days the three would finish a little before 4 days.
- (d)10 days — C would do 4.8 units a day, making 11.8 units for the three, short of the 12 a day that finishes 48 units in 4 days.
Concept
In work and time, add rates, not days. A job done in 16 days means 1⁄16 of it each day.
Taking the total work as the LCM of the given days (48) makes every rate a whole number: A 3, B 4, all three 12. The missing worker's rate is the team's rate minus the known rates, and his time is the total work divided by that rate.
Key facts
- Rate = 1 ⁄ time: here A 1⁄16, B 1⁄12 and all three 1⁄4 of the job a day.
- 1⁄4 − 1⁄16 − 1⁄12 = 12⁄48 − 3⁄48 − 4⁄48 = 5⁄48.
- 48⁄5 = 9.6 = 9 3⁄5 days.
Study next
Common traps
- Converting 48⁄5 carelessly: the remainder is 3 out of 5, so 9 3⁄5 = 9.6, not 9½.
- Combining days instead of rates: A and B together take 48⁄7 ≈ 6.86 days, not (16 + 12) ÷ 2 = 14.
14 Sep 2025, 16:00, Quant Q.12 uses this set-up to split wages: A 12 days, B 18 days, all three 5 days, so C's rate is 1⁄5 − 1⁄12 − 1⁄18 = 11⁄180 and his share of ₹7,200 is ₹2,200.
14 Sep 2025, 09:00, Quant Q.17 also finds C alone, from pair rates and a split schedule, keyed 24 days.
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