Time & Work Questions and Answers

Answer: D

Neither 1 nor 2 is correct.

Work is workers times days and stays constant for the same task.

\[ \begin{aligned} 5 \times 12 &= 60 \Rightarrow \tfrac{60}{10} = 6 \text{ days, not } 5 \\ 8 \times 14 &= 112 \Rightarrow \tfrac{112}{4} = 28 \text{ days, not } 30 \end{aligned} \]

Both statements misstate the result of an inverse proportion: doubling the workforce halves the time (12 to 6), and halving it doubles the time (14 to 28).

Answer: C

Both 1 and 2 are correct.

Statement 1: write the daily work rates as a, b, c with a = 2c.

\[ \begin{aligned} a + b &= \tfrac{1}{12},\ \ b + c = \tfrac{1}{15} \\ (a + b) - (b + c) &= c = \tfrac{1}{12} - \tfrac{1}{15} = \tfrac{1}{60} \\ b &= \tfrac{1}{15} - \tfrac{1}{60} = \tfrac{1}{20} \end{aligned} \]

Here a − c = c because a = 2c. So B alone takes 20 days. True.

Statement 2: together Ram and Shyam do \(\tfrac{1}{10} + \tfrac{1}{6} = \tfrac{8}{30}\) a day, so they take \(30/8 = 3.75\) days, which is within 4 days. True.

Answer: C

All three statements are correct.

Statement 1: \(\tfrac{1}{10} + \tfrac{1}{15} = \tfrac{3 + 2}{30} = \tfrac{1}{6}\), so together they take 6 days.

Statement 2: the job is \(6 \times 8 = 48\) worker-days, so 3 workers need \(48 / 3 = 16\) days.

Statement 3: if A does twice B's work per day, A finishes the same job in half B's time, since time is inversely proportional to efficiency.

Each statement applies the inverse relation between rate and time correctly, so the answer is all three.

Answer: B

The son alone would take \(9\frac{1}{11}\) days.

Work out how much of the field each person ploughs in one day and subtract the parents' share from the family's total.

\[ \begin{aligned} \text{son} &= \frac{1}{5} - \frac{1}{20} - \frac{1}{25} \\ &= \frac{20 - 5 - 4}{100} \\ &= \frac{11}{100} \end{aligned} \]

So the son ploughs \(\frac{11}{100}\) of the field a day and needs \(\frac{100}{11} = 9\frac{1}{11}\) days.

Check that the three together finish in 5 days:

\[ \begin{aligned} \frac{1}{20} + \frac{1}{25} + \frac{11}{100} &= \frac{5 + 4 + 11}{100} \\ &= \frac{20}{100} = \frac{1}{5} \end{aligned} \]

The other options differ only in the whole number, so the subtraction alone decides them.

Answer: A

Working together they finish in 20 days.

A is twice as efficient as B, so B takes twice as long as A. If A takes \(x\) days, B takes \(2x\), and the difference is 30 days:

\[ \begin{aligned} 2x - x &= 30 \Rightarrow x = 30 \\ \text{A} &= 30 \text{ days}, \ \text{B} = 60 \text{ days} \end{aligned} \]

\[ \begin{aligned} \frac{1}{30} + \frac{1}{60} &= \frac{3}{60} \\ &= \frac{1}{20} \end{aligned} \]

So together they do one-twentieth of the work a day and need 20 days.

60 days is B's time working alone. 40 and 80 days are longer than A's own 30 days, which is impossible once B helps.

Answer: D

The wrong option is 48 men are employed.

Take a man's daily work as 5 units and a woman's as 4 (ratio 5 : 4).

\[ \begin{aligned} \text{work} &= 6 \times (12 \times 5 + 20 \times 4) \\ &= 6 \times 140 = 840 \\ \text{per day in 3 days} &= 840/3 = 280 \end{aligned} \]

24 men and 40 women give 120 + 160 = 280, 56 men give 280, and 70 women give 280, so all three finish in 3 days. 48 men give only 240 units a day, so they cannot finish in 3 days.

Answer: B

Rindia can do a job in 10 days.
So efficiency of Rindia = 100/10 = 10%
Similarly, Rakesh's efficiency = 100/5 = 20%
Combined efficiency of Rindia + Rakesh per day becomes = 20 + 10 = 30 %
Now, we have to find out the number of days taken by both Rindia and Rakesh to do 100% work,
Since they can do 30% work in 1 day,
So, they will 100% work in 100/30 = 3.33 days

Answer: D

A completes the work in 30 days. A's one day work will be 1/30 of the work. B's one day work will be 1/45 of the work.
Both work together, in one day, 1/30 + 1/45 of the work will get over.
In one day 75/1350 of the work will get over. Which means the work will get over in 1350/75 days. The work will get completed in 18 days.

Answer: B

Together, A & B will finish the work in 7.2 days.

Answer: C

A completes the work in 24 days. A's one day work will be 1/24 of the work.
B's one day work will be 1/12 of the work.
Both work together, in one day, 1/24 + 1/12 of the work will get over.
In one day 36/288 of the work will get over. Which means the work will get over in 288/36 days.
The work will get completed in 8 days.