Arithmetic

Time & Work

Medium

Anil can paint a house in $60$ days while Bimal can paint it in $84$ days. Anil starts painting and after $10$ days, Bimal and Charu join him. Together, they complete the painting in $14$ more days. If they are paid a total of Rs. $21000$ for the job, then the share of Charu, in INR, proportionate to the work done by him, is

$9100$

$9150$

$9000$

$9200$

✅ Correct Option: 1

We have three painters working on a house:

Anil can complete the entire house in 60 days

Bimal can complete the entire house in 84 days

Charu's ability is unknown (we need to find it)

The work schedule is:

Anil works alone for 10 days

Then all three work together for 14 more days

Total payment: Rs. 21000

When dealing with work problems, we assume the total work is a convenient number that makes calculations easier. The LCM of the given time periods works perfectly.

LCM of 60 and 84:

60 = $2^2 \times 3 \times 5$

84 = $2^2 \times 3 \times 7$

LCM = $2^2 \times 3 \times 5 \times 7 = 420$

Total Work = 420 units

Now we can find each person's work rate:

Anil's rate = $420 \div 60 = 7$ units per day

Bimal's rate = $420 \div 84 = 5$ units per day

Charu's rate = Let's call it $x$ units per day

Phase 1: Anil works alone (10 days)

Work done by Anil = $7 \times 10 = 70$ units

Phase 2: All three work together (14 days)

Combined rate = $7 + 5 + x = (12 + x)$ units per day

Work done by all three together = $(12 + x) \times 14 = 14(12 + x)$ units

Total work done = Total work required

Work done in Phase 1 + Work done in Phase 2 = 420 units

$70 + 14(12 + x) = 420$

$70 + 168 + 14x = 420$

$238 + 14x = 420$

$14x = 420 - 238 = 182$

$x = 13$ units per day

So Charu can do 13 units of work per day.

Anil's total work:

Phase 1: $7 \times 10 = 70$ units

Phase 2: $7 \times 14 = 98$ units

Total = 168 units

Bimal's total work:

Phase 1: 0 units (didn't work)

Phase 2: $5 \times 14 = 70$ units

Total = 70 units

Charu's total work:

Phase 1: 0 units (didn't work)

Phase 2: $13 \times 14 = 182$ units

Total = 182 units

Work ratio = Anil : Bimal : Charu = 168 : 70 : 182

Dividing each by 2: 84 : 35 : 91

Total parts = $84 + 35 + 91 = 210$ parts

Charu's share = $\frac{91}{210} \times 21000$

= $\frac{91 \times 21000}{210}$

= $91 \times 100 =$ Rs. 9100

Charu's share = Rs. 9100

CAT 2020 Slot 3

A contractor agreed to construct a $6$ km road in $200$ days. He employed $140$ persons for the work. After $60$ days, he realized that only $1.5$ km road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?

CAT 2022 Slot 3

A group of $N$ people worked on a project. They finished $35 \%$ of the project by working $7$ hours a day for $10$ days. Thereafter, $10$ people left the group and the remaining people finished the rest of the project in $14$ days by working $10$ hours a day. Then the value of $N$ is

CAT 2024 Slot 1

Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is

CAT 2023 Slot 1

The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression. Kamal takes twice as much time as Amal to do the same amount of job. If Amal and Sunil work for $4$ days and $9$ days, respectively, Kamal needs to work for $16$ days to finish the remaining job. Then the number of days Sunil will take to finish the job working alone, is

CAT 2021 Slot 3

One day, Rahul started a work at $9$ AM and Gautam joined him two hours later. They then worked together and completed the work at $5$ PM the same day. If both had started at $9$ AM and worked together, the work would have been completed $30$ minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is

2025 Slot 1

Arun, Varun and Tarun, if working alone, can complete a task in 24, 21, and 15 days, respectively. They charge Rs 2160, Rs 2400, and Rs 2160 per day, respectively, even if they are employed for a partial day. On any given day, any of the workers may or may not be employed to work. If the task needs to be completed in 10 days or less, then the minimum possible amount, in rupees, required to be paid for the entire task is

Solution

Related questions:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)