Time & Work Questions and Answers

Answer: B

They will take 6 days.

The whole work is \(45 \times 16 = 720\) man-days. In the first six days, 45 men do \(45 \times 6 = 270\) man-days, leaving 450 man-days. Now \(45 + 30 = 75\) men work:

\[ \frac{450}{75} = 6\ \text{days} \]

10 days is the time the original 45 men would still have needed, and 8 and 12 days do not fit the man-day total.

Answer: D

The fraction of the work left is 23/42. A does \(\frac{1}{14}\) of the work in a day and B does \(\frac{1}{24}\), so together they do \[ \frac{1}{14} + \frac{1}{24} = \frac{12 + 7}{168} \] \[ \frac{12 + 7}{168} = \frac{19}{168} \] In 4 days they do \(\frac{76}{168} = \frac{19}{42}\). The work left is \[ 1 - \frac{19}{42} = \frac{23}{42} \] The fraction 19/42 is the work done and not the work left, and the others, 18/42, 45/42 and 33/42, do not match.

Another way: take 168 units of work, the lcm of 14 and 24. A does 12 units and B 7 a day, so 4 days make 76 units, and 92 of 168 are left, which is 23/42.

Answer: C

C alone can do the job in 9 days. A does \(\frac{1}{18}\) of the work in a day and B does \(\frac{1}{12}\), together \(\frac{5}{36}\). With C's help the whole job takes 4 days, so the three together do \(\frac{1}{4}\) per day. \[ \frac{1}{4} - \frac{5}{36} = \frac{9 - 5}{36} \] \[ \frac{4}{36} = \frac{1}{9} \] So C does \(\frac{1}{9}\) of the job per day and needs 9 days alone. The options 13, 11 and 10 days would give C a daily share of less than 1/9.

Answer: B

The work is completed in \(10\frac{7}{9}\) days. Aakash does 1/8 of the work in a day and Bhanu does 1/18, so two days (one of each) complete \[\frac{1}{8} + \frac{1}{18} = \frac{13}{72}\] Five such pairs, 10 days, complete 65/72 of the work, leaving 7/72. On the eleventh day Aakash works first, and he does 9/72 in a full day, so he needs \[\frac{7/72}{9/72} = \frac{7}{9}\] of a day. The total is \(10\frac{7}{9}\) days. Starting with Bhanu or counting a full day would give the other values listed.

Answer: D

U works every day, and V and W also help on every third day. In a block of three days, U does 3/20 of the work, and on the third day V and W add 1/30 + 1/60 = 1/20.

\[ \tfrac{3}{20} + \tfrac{1}{20} = \tfrac{4}{20} \]

\[ \tfrac{4}{20} = \tfrac{1}{5} \text{ per 3 days} \]

So the work needs 5 blocks of 3 days, which is 15 days. Because the work ends exactly at the end of the fifth block, there is no extra partial block, and the answer is 15 days.

Answer: B

Equal work is done in the two cases, so 10 days of 6 men and 8 women equal 8 days of 5 men and 15 women.

\[ 10(6m + 8w) = 8(5m + 15w) \]

\[ 20m = 40w \Rightarrow m = 2w \]

The whole work is 10 x (12w + 8w) = 200w. And 17 men and 16 women make 34w + 16w = 50w per day, so they take 200 / 50 = 4 days. The options 3, 6 and 7 do not fit this rate.

Answer: C

They finish in 24 days. In one day A does 1/40 of the work and B does 1/60.

So the work takes 24 days together. 30, 32 and 25 days are wrong because working together must be faster than A alone, and 25 days would need a combined rate of 1/25.

Check with a total of 120 units of work: A does 3 units a day and B does 2, so together they do 5 units a day, and 120 / 5 = 24 days. This also shows the answer is shorter than either person's time alone, which is a quick test for combined-work questions.

Answer: C

They finish in 12 days. In a day Raju does 1/20 of the job and Vishal 1/30.

The combined time is 12 days. 10 and 6 days would be too fast for these rates, and 25 days is slower than Raju alone.

Check with a total of 60 units of work: Raju does 3 units a day and Vishal 2, so together they do 5 units a day, and 60 / 5 = 12 days. The answer lies between half of the faster person's time (10) and the faster person's own time (20), which agrees with 12.

Answer: B

They finish in 8 days. Their daily shares are 1/30, 1/20 and 1/24, and \[ \frac{1}{30} + \frac{1}{20} + \frac{1}{24} \] \[ = \frac{4 + 6 + 5}{120} = \frac{1}{8} \] so together they take 8 days.

5, 6 and 7 days would need daily shares of 1/5, 1/6 and 1/7, more than the combined 1/8.

Answer: D

C alone would take 240 days. In 20 days A and B finish 20 × (1/120 + 1/150) = 20 × 9/600 = 0.3. A alone works 12 more days for 12/120 = 0.1. That leaves 1 - 0.4 = 0.6, which A and C finish in 48 days: \[ 48\left(\frac{1}{120} + \frac{1}{c}\right) = 0.6 \] \[ \frac{48}{c} = 0.2 \Rightarrow c = 240 \]

200, 210 and 220 days do not satisfy the equation.

The work completed in the first 20 days (0.3) and the next 12 days (0.1) leaves 0.6 for the final stage of 48 days.