Time and Work Practice Test 1

Solution: The correct answer is 24 \( \frac{2}{5} \).

Explanation:

To solve this problem, we use the concept of LCM to find the total work, followed by calculating the work done by A and B over the 5 days, and finally determining the time required for B to complete the remaining work.

Step 1: Calculate the total work using LCM.
A can complete the work in 25 days and B in 30 days. The LCM of 25 and 30 is 150, so the total work is 150 units.

Step 2: Determine the efficiency of A and B.
– A’s efficiency = \( \frac{150}{25} = 6 \) units/day
– B’s efficiency = \( \frac{150}{30} = 5 \) units/day

Step 3: Calculate the work done in 5 days.
– Day 1: A does 6 units
– Day 2: B does 5 units
– Day 3: A does 6 units
– Day 4: B does 5 units
– Day 5: A does 6 units
Total work done in 5 days = 6 + 5 + 6 + 5 + 6 = 28 units

Step 4: Determine the remaining work and time required for B to finish it.
– Remaining work = 150 – 28 = 122 units
– Time taken by B to complete the remaining work = \( \frac{122}{5} = 24.4 \) days or 24 \( \frac{2}{5} \) days

Therefore, B will take 24 \( \frac{2}{5} \) days to finish the remaining work.

Solution: The correct answer is 27 days.

Explanation:

– Let the number of days taken by Q to complete the work be \( x \).
– P’s time to complete the work = \( \frac{x}{2} \).
– Given \( \frac{x}{2} = x – 40 \). Solving this gives \( x = 80 \) days.
– So, P takes 40 days to complete the work.

– Combined efficiency of P and Q = \( \frac{1}{40} + \frac{1}{80} = \frac{3}{80} \).
– Time taken together = \( \frac{80}{3} = 26.67 \) days, which rounds off to 27 days.

Solution: The correct answer is 18 \( \frac{3}{4} \) days.

Explanation:

– Virat’s efficiency (work per day) = \( \frac{1}{30} \) of the work.
– Daniel’s efficiency = 160% of Virat’s efficiency = \( 1.6 \times \frac{1}{30} = \frac{4}{75} \) of the work per day.

– Time taken by Daniel to complete the work = \( \frac{1}{\frac{4}{75}} = \frac{75}{4} = 18.75 \) days = 18 \( \frac{3}{4} \) days.

Solution: The correct answer is 2 \( \frac{2}{59} \) hours.

Explanation:

– Monika’s efficiency = \( \frac{1}{6} \) work/hour.
– Anita’s efficiency = \( \frac{1}{8} \) work/hour.
– Manju’s efficiency = \( \frac{1}{5} \) work/hour.

– Combined efficiency = \( \frac{1}{6} + \frac{1}{8} + \frac{1}{5} = \frac{59}{120} \) work/hour.
– Time taken to complete the work together = \( \frac{120}{59} \approx 2 \frac{2}{59} \) hours.

Solution: The correct answer is 16 days.

Explanation:

– A’s work per day = \( \frac{1}{12} \) of the work, but A works only for 8 hours.
– A’s efficiency per hour = \( \frac{1}{96} \). B’s efficiency = \( \frac{1}{192} \).

– B’s total work per day = \( 12 \times \frac{1}{192} = \frac{1}{16} \) of the work.
– B takes 16 days to finish the work.

Solution: The correct answer is 32 days.

Explanation:

– Ajay’s efficiency is \( \frac{1}{32} \) of the work per day, as he can complete the work alone in 32 days.
– Let Bharat’s efficiency be \( x \). Therefore, Bharat completes \( x \) of the work per day.

Since Bharat starts the work and they work on alternate days, in 8 days Bharat will work for 4 days, and Ajay will also work for 4 days.

The total work done by Ajay in 4 days = \( 4 \times \frac{1}{32} = \frac{4}{32} = \frac{1}{8} \) of the total work.

The total work done by Bharat in 4 days = \( 4x \) (since Bharat works for 4 days).

According to the problem, the total work done by both Ajay and Bharat together in 8 days is equal to the entire work:

\( 4x + \frac{1}{8} = 1 \)

Solve for \( x \):

\( 4x = 1 – \frac{1}{8} = \frac{8}{8} – \frac{1}{8} = \frac{7}{8} \)

\( x = \frac{7}{32} \)

Bharat’s efficiency is \( \frac{7}{32} \) of the work per day. Therefore, the number of days Bharat alone would take to complete 1 unit of work is:

\( \frac{1}{\frac{7}{32}} = \frac{32}{7} \) days.

Since the question asks for the time Bharat would take to complete 7 times the work:

Time taken = \( 7 \times \frac{32}{7} = 32 \) days.

Therefore, Bharat alone can finish 7 times the same work in **32 days**.

Solution: The correct answer is \( \frac{1}{5} \).

Explanation:

– A’s efficiency = \( \frac{1}{12} \) of the work per day.
– B’s efficiency = \( \frac{1}{15} \) of the work per day.
– C’s efficiency = \( \frac{1}{20} \) of the work per day.

– Combined efficiency = \( \frac{1}{12} + \frac{1}{15} + \frac{1}{20} = \frac{12}{60} = \frac{1}{5} \) of the work per day.

– Work done in 4 days = \( 4 \times \frac{1}{5} = \frac{4}{5} \).

– Remaining work = \( 1 – \frac{4}{5} = \frac{1}{5} \).

Solution: The correct answer is 38 \( \frac{1}{12} \) days.

Explanation:

30, 40, 50 L.C.M = 600 (Total Work)
– A’s efficiency = \( \frac{600}{30} \)=20 of the work per day.
– B’s efficiency = \( \frac{600}{40} \)=15 of the work per day.
– C’s efficiency = \( \frac{600}{50} \)=12 of the work per day.

– Combined work done in 3 days = \( \frac{47}{600} \) of the work.

– After 12 cycles (36 days), \( \frac{564}{600} \) of the work is done, leaving \( \frac{36}{600} \) work remaining.

– On Day 37, A completes \( \frac{20}{600} \), leaving \( \frac{16}{600} \) work.
– On Day 38, B completes \( \frac{15}{600} \), leaving \( \frac{1}{600} \) work.
– On Day 39, C completes the remaining \( \frac{1}{600} \) in \( \frac{1}{12} \) day.

– Total days taken = 36 + 1 + 1 + \( \frac{1}{12} \) = 38 \( \frac{1}{12} \) days.

Solution: The correct answer is 48 days.

Explanation:

– Ravi’s efficiency = \( \frac{1}{40} \) of the work per day.
– Sudha’s efficiency = \( \frac{1}{60} \) of the work per day.

– Combined work done in 2 days (1 cycle) = \( \frac{1}{60} + \frac{1}{40} = \frac{5}{120} = \frac{1}{24} \) of the work.

– In 48 days (24 cycles), they complete \( 24 \times \frac{1}{24} = 1 \) unit of work, meaning the entire work is completed.

Solution: The correct answer is 15 \( \frac{5}{13} \) days.

Explanation:

40, 25 l.C.M = 200
– 15 man’s efficiency = \( \frac{200}{40} \)=8 of the work per day.
– 25 woman’s efficiency = \( \frac{200}{25} \)=5 of the work per day.
total efficiency=8+5=13

– Combined efficiency of 15 men and 25 women = \( \frac{1}{25} + \frac{1}{40} = \frac{13}{200} \) of the work per day.

– Total time taken = \( \frac{200}{13} = 15 \frac{5}{13} \) days.