Question

A person A can complete a work in 12 minutes. The persons B and C are respectively 25% and $33\frac{1}{3}%$ more efficient than A. If all three work together, the number of minutes they take to complete the work is _____.

• A. 29 minutes
• B. 24 minutes
• C. $\frac{72}{23}$ minutes
• D. $\frac{89}{32}$ minutes

Hint:

Convert efficiency changes into fractions first, then add rates.

Answer 1

The Correct Option is C

Concept: Efficiency is inversely proportional to time.
Step 1: Efficiency of A.
\[ A = \frac{1}{12} \]
Step 2: Efficiency of B and C.
\[ B = 1.25 \times \frac{1}{12} = \frac{5}{4} \cdot \frac{1}{12} = \frac{5}{48} \] \[ C = \frac{4}{3} \times \frac{1}{12} = \frac{1}{9} \]
Step 3: Total efficiency.
\[ {Total} = \frac{1}{12} + \frac{5}{48} + \frac{1}{9} \] Take LCM = 144: \[ = \frac{12 + 15 + 16}{144} = \frac{43}{144} \]
Step 4: Time taken.
\[ {Time} = \frac{144}{43} = \frac{72}{23} { minutes} \]
Hence, the required time is $\frac{72{23}$ minutes.