A takes twice as long as B or thrice as long as C to finish a job. Working together, they finish in 2 days. In how many days can B alone finish the job?

Problem restatementRelate individual times of A, B, C using the given proportional information and their joint time (2 days) to find B's solo time.

Given data

• T_A = 2T_B = 3T_C.
• Working together, A + B + C finish in 2 days → joint rate = 1/2 job/day.

Concept/ApproachLet T_B = x days → T_A = 2x. Also T = 3T → T = (2x)/3. Convert times to rates and add.

Step-by-step calculation a = 1/T = 1/(2x) b = 1/T = 1/x c = 1/T = 1/((2x)/3) = 3/(2x) a + b + c = 1/(2x) + 1/x + 3/(2x) = (1/2 + 1 + 3/2)/x = 3/x Given 3/x = 1/2 → x = 6

VerificationB alone takes x = 6 days. Check: T = 12 days, T = 4 days. Rates add: 1/12 + 1/6 + 1/4 = (1 + 2 + 3)/12 = 6/12 = 1/2 job/day → 2 days total.

Common pitfalls

• Confusing time ratios with rate ratios; remember rate is inverse of time.
• Adding times instead of rates.

Final Answer6 days