TANCET 2023 Solved Papers

Concept:Use the given efficiency ratios to find the total work, then compute the remaining work and the required time.Explanation:Let the efficiency of B be $1$ unit per day.A is 25% more efficient than B, so efficiency of A is $1 + \frac{1}{4} = \frac{5}{4}$ units per day.C is 25% less efficient than B, so efficiency of C is $1 - \frac{1}{4} = \frac{3}{4}$ units per day.Combined efficiency of A, B and C is $\frac{5}{4} + 1 + \frac{3}{4} = 3$ units per day.All three together finish the work in 24 days, so total work is $3 \times 24 = 72$ units.Efficiency of B and C together is $1 + \frac{3}{4} = \frac{7}{4}$ units per day.Work done by B and C in 32 days is $\frac{7}{4} \times 32 = 56$ units.Remaining work is $72 - 56 = 16$ units.With double efficiency, B works at $2 \times 1 = 2$ units per day.Time needed by B alone is $\frac{16}{2} = 8$ days.Answer:$8$ days, i.e., Option A.