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

Entered answer:

✅ Correct Answer: 6

Renu can complete the work in 15 days working 4 hours/day
Seema can complete the work in 8 days working 5 hours/day

Attribute	Renu	Seema
Days to Complete	15	8
Hours per Day	4	5
Total Hours	60	40

To work with whole numbers, we assume total work = LCM(60, 40) = 120 units

Attribute	Renu	Seema
Days to Complete	15	8
Hours per Day	4	5
Total Hours	60	40
Total Work	120	120

Rate = Total Work ÷ Total Hours

Attribute	Renu	Seema
Days to Complete	15	8
Hours per Day	4	5
Total Hours	60	40
Rate (units/hour)	120 ÷ 60 = 2	120 ÷ 40 = 3
Total Work	120	120

New working conditions from the problem:

Renu works 2 hours per day
Seema works double the hours of Renu → 2 × 2 = 4 hours per day
Renu works double the days of Seema

Attribute	Renu	Seema
Rate (units/hour)	2	3
New Hours per Day	2	4
Daily Work Output	2 × 2 = 4	3 × 4 = 12
Days Working	2x	x

We have to find working days of Seema, hence we have to find $x$

Attribute	Renu	Seema
Rate (units/hour)	2	3
New Hours per Day	2	4
Daily Work Output	4	12
Days Working	2x	x
Total Work Done	4 × 2x = 8x	12 × x = 12x

Since together they complete the entire work:

Renu's work + Seema's work = Total work

From the table:

$8x + 12x = 120$

Solving:

$20x = 120$

$x = 120 ÷ 20$

$x = 6$

Answer: Seema will work for 6 days

CAT 2018 Slot 1

Humans and robots can both perform a job but at different efficiencies. Fifteen humans and five robots working together take thirty days to finish the job, whereas five humans and fifteen robots working together take sixty days to finish it. How many days will fifteen humans working together (without any robot) take to finish it?

CAT 2019 Slot 1

Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in $13$ days, then how many men can finish the job in $13$ days?

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

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 2019 Slot 1

At their usual efficiency levels, $A$ and $B$ together finish a task in $12$ days. If $A$ had worked half as efficiently as she usually does, and $B$ had worked thrice as efficiently as he usually does, the task would have been completed in $9$ days. How many days would $A$ take to finish the task if she works alone at her usual efficiency?

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

Solution

Related questions:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)