A and B can complete a job together in 7 days. A is 1¾ times as efficient as B. In how many days can A alone complete the job?

Problem restatementGiven the joint time and relative efficiency, find A’s solo time.

Given data

• A : B efficiency = 1¾ : 1 = 7 : 4
• Joint time = 7 days

Concept/ApproachLet B’s rate be b. Then A’s rate is (7÷4)b. Use their combined rate to compute b and then A’s rate.

Step-by-step calculationCombined rate = 1÷7 per day = b + (7÷4)b = (11÷4)b(11÷4)b = 1÷7 ⇒ b = 4÷77A’s rate = (7÷4)b = 7÷77 = 1÷11 per dayTime for A alone = 11 days

Verification/AlternativeCheck: A + B rate = 1÷11 + 4÷77 = 7÷77 + 4÷77 = 11÷77 = 1÷7.

Common pitfallsDo not confuse ratio of efficiencies with ratio of times (they are inversely related).

Final Answer11 days