Work & Wages Questions and Answers

Answer: B

The ratio of their efficiencies is inversely proportional to the time they take. Ratio of time A:B = 30:40 = 3:4. Ratio of efficiency A:B = 4:3. The wages will be shared in the ratio of efficiency. B's share = \(\frac{3}{4+3} \times 7000 = \frac{3}{7} \times 7000 = 3000\). B's share is Rs. 3000.

Answer: A

The remaining food was supposed to last for 500 men for 27-3 = 24 days. Total remaining food = \(500 \times 24\) man-days. Now, the number of men is \(500+300=800\). The food will last for \((500 \times 24) / 800 = 12000 / 800 = 15\) days.

Answer: A

Let B do W work in T time. Then A does W/2 work in 3T/4 time. B's rate = W/T. A's rate = (W/2)/(3T/4) = 2W/3T. The ratio of their rates A:B = (2W/3T) : (W/T) = 2/3 : 1 = 2:3. Combined rate is 5 units. Total work = \(5 \times 18 = 90\) units. B's rate is 3 units/day. Time for B alone = 90/3 = 30 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.

\[ \frac{1}{10} + \frac{1}{12} - \frac{1}{20} = \frac{6 + 5 - 3}{60} = \frac{8}{60} = \frac{2}{15} \]

\[ t = \frac{15}{2} = 7.5 \text{ h} = 7 \text{ hr } 30 \text{ min} \]

Answer: C

Let the total work be LCM(45,40)=360 units. A's rate=8, B's rate=9 units/day. B worked alone for the last 23 days, so work done by B alone = \(23 \times 9 = 207\) units. Work done by A and B together = \(360 - 207 = 153\) units. Combined rate of A and B = 8+9=17 units/day. Time they worked together = 153/17 = 9 days. So, A left after 9 days.

Answer: A

Combined one day's work = 1/3. Man's one day work = 1/6. Boy's one day work = 1/18. Woman's one day work = \(1/3 - (1/6+1/18) = 1/3 - (3+1)/18 = 1/3 - 4/18 = 1/3 - 2/9 = (3-2)/9 = 1/9\). A woman alone will take 9 days.

Answer: B

50% more efficient means X does the work in \( \tfrac{2}{3} \) of Y's time.

\[ t_{X} = \frac{2}{3} \times 30 = 20 \text{ days} \]

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

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

Answer: B

Correct answer: Rs. 300

Wages divide in the ratio of work actually done, which for a common period is the ratio of the daily rates.

All three together complete the job in 5 days, so their combined rate is \(\tfrac{1}{5}\). Subtracting A and B gives C’s rate:

\[\frac{1}{5} - \frac{1}{15} - \frac{1}{12} = \frac{12}{60} - \frac{4}{60} - \frac{5}{60} = \frac{3}{60} = \frac{1}{20}\]

So the rates are \(\tfrac{1}{15} : \tfrac{1}{12} : \tfrac{1}{20}\), which on multiplying by 60 becomes \(4 : 5 : 3\).

\[\text{C’s share} = \frac{3}{4+5+3} \times 1200 = \frac{3}{12} \times 1200 = 300\]

Answer: C

Correct answer: 7.2 days

Add the daily rates rather than the times.

\[\frac{1}{12} + \frac{1}{18} = \frac{3}{36} + \frac{2}{36} = \frac{5}{36}\]

Working at five thirty-sixths of the job per day, they need

\[\frac{36}{5} = 7.2 \text{ days}\]

Answer: C

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

\[ \frac{1}{16} + \frac{1}{12} + \frac{1}{C} = \frac{1}{4} \]

\[ \frac{1}{C} = \frac{12}{48} - \frac{3 + 4}{48} = \frac{5}{48} \]

\[ C = \frac{48}{5} = 9\tfrac{3}{5} \text{ days} \]