CAT 2024 Slot 1 QA Question 21

Type-in-the-answer (no negative marking) · Arithmetic · Time & Work · Try it, then check the answer and solution below.

CAT 2024 Slot 1QAArithmetic • Time & WorkModerate

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

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Official Convenor Answer Key: 6

Verified Solution:

### Core Concept The problem involves calculating the work rates of two individuals, Renu and Seema, and then combining their efforts under specific conditions to determine the number of days Seema will work. The key formula used is:

\text{Work} = \text{Rate} \times \text{Time}

### Step-by-Step Solution

Calculate Total Work Hours:

Renu's total work hours:

15 \text{ days} \times 4 \text{ hours/day} = 60 \text{ hours}

Seema's total work hours:

8 \text{ days} \times 5 \text{ hours/day} = 40 \text{ hours}

Determine Individual Rates:

Renu's rate:

\frac{1 \text{ task}}{60 \text{ hours}} = \frac{1}{60} \text{ per hour}

Seema's rate:

\frac{1 \text{ task}}{40 \text{ hours}} = \frac{1}{40} \text{ per hour}

Set Up Working Conditions:

Renu works 2 hours per day.

Seema works double the hours per day as Renu:

2 \times 2 = 4 \text{ hours/day}

Let the number of days Seema works be

D

. Then, Renu works

2D

days.

Calculate Total Hours Worked:

Renu's total hours:

2 \text{ hours/day} \times 2D \text{ days} = 4D \text{ hours}

Seema's total hours:

4 \text{ hours/day} \times D \text{ days} = 4D \text{ hours}

Calculate Work Done:

Renu's work:

\frac{1}{60} \times 4D = \frac{4D}{60} = \frac{D}{15}

Seema's work: \(\frac{

Answer and solution

Answer: 6

\text{Work} = \text{Rate} \times \text{Time}

### Step-by-Step Solution

Calculate Total Work Hours:

Renu's total work hours:

15 \text{ days} \times 4 \text{ hours/day} = 60 \text{ hours}

Seema's total work hours:

8 \text{ days} \times 5 \text{ hours/day} = 40 \text{ hours}

Determine Individual Rates:

Renu's rate:

\frac{1 \text{ task}}{60 \text{ hours}} = \frac{1}{60} \text{ per hour}

Seema's rate:

\frac{1 \text{ task}}{40 \text{ hours}} = \frac{1}{40} \text{ per hour}

Set Up Working Conditions:

Renu works 2 hours per day.

Seema works double the hours per day as Renu:

2 \times 2 = 4 \text{ hours/day}

Let the number of days Seema works be

D

. Then, Renu works

2D

days.

Calculate Total Hours Worked:

Renu's total hours:

2 \text{ hours/day} \times 2D \text{ days} = 4D \text{ hours}

Seema's total hours:

4 \text{ hours/day} \times D \text{ days} = 4D \text{ hours}

Calculate Work Done:

Renu's work:

\frac{1}{60} \times 4D = \frac{4D}{60} = \frac{D}{15}

Seema's work: \(\frac{

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