Work & Wages Questions and Answers

Answer: C

A's share is ₹ 400.

Payment is shared in proportion to the work each does. In the 5 days the work takes, A does 5/12 of it and B does 5/15 = 1/3:

\[ \begin{aligned} C &= 1 - \tfrac{5}{12} - \tfrac{4}{12} = \tfrac{3}{12} \\ A &: B : C = 5 : 4 : 3 \end{aligned} \]

A's share is \(960 \times 5/12 = 400\), with B getting 320 and C 240. Sharing by the ratio of days (12 : 15) instead of work done gives the wrong amounts.

Answer: B

He works 175 hours.

Regular hours in 4 weeks are 4 × 5 × 8 = 160. The earnings separate into regular pay and overtime:

\[ \begin{aligned} 160 \times 2.40 &= 384 \\ 432 - 384 &= 48 \\ 48 \div 3.20 &= 15 \text{ overtime hours} \end{aligned} \]

So he works 160 + 15 = 175 hours. 160 counts only the regular hours, and 180 and 195 would mean more overtime than Rs. 48 pays for.

Answer: A

The cost is ₹ 67.50.

A takes \(\frac{63}{3.50} = 18\) days and B takes \(\frac{75}{2.50} = 30\) days to do the work alone. Together they do

\[ \begin{aligned} \frac{1}{18} + \frac{1}{30} &= \frac{5 + 3}{90} = \frac{8}{90} \\ \text{days} &= \frac{90}{8} = 11.25 \end{aligned} \]

Their combined daily wage is ₹ 6, so the cost is \(11.25 \times 6 = 67.50\). Averaging the two totals gives ₹ 69, and the other options do not follow from the times.

Answer: A

C's share is 1,440 rupees.

In 12 hours A does \(\frac{12}{27} = \frac{4}{9}\) of the task and B does \(\frac{12}{54} = \frac{2}{9}\). C must do the rest:

\[ \begin{aligned} 1 - \tfrac{4}{9} - \tfrac{2}{9} &= \tfrac{3}{9} = \tfrac{1}{3} \\ \text{C's share} &= \tfrac{1}{3} \times 4320 = 1440 \end{aligned} \]

Payment is divided in proportion to work done. 1,920 is A's share and 960 B's.

Answer: B

Work in rates: someone who finishes a job in \( n \) days does \( \tfrac{1}{n} \) of it a day, and rates add.

\[ \frac{1}{10} + \frac{1}{15} = \frac{3 + 2}{30} = \frac{1}{6} \]

\[ t = 6 \text{ days} \]

Answer: B

Total work can be assumed as the LCM of 12, 15, and 20, which is 60 units. A's efficiency = 60/12 = 5 units/day. B's efficiency = 60/15 = 4 units/day. C's efficiency = 60/20 = 3 units/day. Together, their efficiency = 5+4+3 = 12 units/day. Time taken to complete the work together = Total work / Combined efficiency = 60 / 12 = 5 days.

Answer: A

Work done by (A+B+C) in 1 day = 1/4. Work done by A in 1 day = 1/16. Work done by B in 1 day = 1/12. Work done by C in 1 day = \(1/4 - (1/16 + 1/12) = 1/4 - (3+4)/48 = 1/4 - 7/48 = (12-7)/48 = 5/48\). So, C alone can do the work in 48/5 = 9.6 days.

Answer: C

Twice the efficiency means half the time, so B takes twice as long as A.

\[ 2 \times 30 = 60 \text{ days} \]

Answer: B

Work in rates: someone who finishes a job in \( n \) days does \( \tfrac{1}{n} \) of it a day, and rates add.

\[ \frac{1}{20} + \frac{1}{30} = \frac{3 + 2}{60} = \frac{1}{12} \]

\[ t = 12 \text{ minutes} \]

Answer: D

Let the efficiency of B be x units/day. Then the efficiency of A is 2x units/day. Their combined efficiency is 3x units/day. Total work = Efficiency * Time = 3x * 12 = 36x units. Time taken by B alone = Total work / B's efficiency = 36x / x = 36 days.