Question:
Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is
Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is
Updated On: Jan 13, 2026
- 30
- 36
- 70
- None of Above
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Let's assume W be the total amount of work.
And g and s be the efficiencies of Gautam and Suhani respectively.
According to the question:
$ \Rightarrow\ g + s = \frac{W}{20} $ (1 day work) ……. (i)
And given that Gautam is doing only 60%: $ \frac{3g}{5} $
Suhani is doing 150%: $ \frac{3s}{2} $
Now, using this, we get:
$ \Rightarrow\ \frac{3g}{5} + \frac{3s}{2} = \frac{W}{20} $ (1 day work)
$ \Rightarrow\ g + s = \frac{3g}{5} + \frac{3s}{2} $
$ \Rightarrow\ \frac{s}{g} = \frac{4}{5} $
This implies that Gautam is more efficient.
By using equation (i), we get:
$ \Rightarrow\ g + \frac{4g}{5} = \frac{W}{20} $
$ \Rightarrow\ \frac{9}{5}g = \frac{W}{20} $
$ \Rightarrow\ g = \frac{W}{36} $
Therefore, Gautam takes 36 days to finish the given work.
So, the correct option is (B) : 36.
Was this answer helpful?
0
3
Top Questions on Time and Work
- If five men can build a house in 27 days, how long will it take nine men to build the same house, assuming they all work at the same rate?
- UCEED - 2026
- Mathematics
- Time and Work
- An artificial swimming pool is circular and water is flowing clockwise at a speed of 3 km/hr. Two swimmers Ayub and Rana start from diametrically opposite points, Ayub in the anticlockwise direction and Rana in the clockwise direction. They first meet at a point such that Ayub has covered 60 m by that time. Their second meeting point is such that Rana has covered another 180 m after the first meeting point. If the speed of Rana in still water is 3 km/hr, find the time taken by Ayub to cover one full circle in the clockwise direction.
- In a multiple-choice examination, there are 20 questions. Each correct answer is worth 4 marks, while 2 marks are to be deducted for every unattempted question. One student receives a total of 46 marks in the examination. However, before releasing the marks, the professor realizes that she has, by mistake, deducted 2 marks for every unattempted question and 1 mark for every wrong answer.
After correction, how many marks will the student get?
- Two buses travel between Jamshedpur and Kolkata in the opposite directions, on the same road. On that road, the maximum allowed speeds are different (but constant) for the opposite directions. Usually, both buses travel at the respective maximum allowed speeds to their respective destinations: the bus from Jamshedpur to Kolkata takes 4 hours, while the bus from Kolkata to Jamshedpur takes 3 hours.
One day, the two buses start at the same time. However, one hour after starting, the bus from Jamshedpur to Kolkata reduces its speed to half of its maximum allowed speed due to congestion on the road.
If both buses do not stop anywhere in between, how many hours after starting do they meet?
- Two trains running at constant speed between Jamshedpur and Kolkata take 3 hours and 4 hours respectively. The train from Jamshedpur halves its speed after running for one hour. How much total time do the trains take to meet?
View More Questions
Questions Asked in CAT exam
- The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.- CAT - 2025
- Para Summary
- The number of distinct integers $n$ for which $\log_{\left(\frac14\right)}(n^2 - 7n + 11)>0$ is:
- CAT - 2025
- Linear Inequalities
- In the set of consecutive odd numbers $\{1, 3, 5, \ldots, 57\}$, there is a number $k$ such that the sum of all the elements less than $k$ is equal to the sum of all the elements greater than $k$. Then, $k$ equals?
- CAT - 2025
- Number Systems
- The number of distinct pairs of integers $(x, y)$ satisfying the inequalities $x>y \ge 3$ and $x + y<14$ is:
- CAT - 2025
- Number Systems
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is:
- CAT - 2025
- Linear Inequalities
View More Questions