Answer:
Anu can do 
of work in one day.
Vinu can do 
of work in one day.
Manu can do 
of work in one day.
On the odd days, Anu and Vinu work together. They together can do 
of work in one day.
On the even days, Manu and Vinu work together. They together can do 
of work in one day.
Therefore, the work was completed in 7 days.
The answer is '7’
Choice D is the correct answer.
CAT 2021 Quant Question
How many three-digit numbers are greater than 100 and increase by 198 when the three digits are arranged in the reverse order?
Answer:
Let’s consider a three-digit number to be ‘abc’.
Given that, three-digit numbers increase by 198 when the three digits are arranged in the reverse order.
100c + 10b + a - 100a - 10b - c = 198
99c - 99a = 198
c - a = 2
So, the difference between the hundreds place digit and the units place digit is 2.
The possible combinations are:
1 _ 3, 2 _ 4, 3 _ 5, 4 _ 6, 5 _ 7, 6 _ 8, 7 _ 9.
We have 10 numbers for each combination.
Hence, the total numbers are 70.
Hence, the answer is ‘70’
CAT 2021 Quant Question
Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faster train is 160 m long and crosses a lamp post in 12 seconds. If the speed of the other train is 6 km/hr less than the faster one, its length, in m, is
A. 184
B. 180
C. 190
D. 192
Answer
The faster train is 160 m long and crosses a lamp post in 12 seconds.
The speed of the faster train = 
Given that, the speed of the other train is 6 km/hr 
less than the faster one. [we can convert speeds from km/h to m/s by multiplying with 5/18]
The speed of the slower train = 
Given that, the two trains cross each other in 14 seconds when running in opposite directions along parallel tracks.
Length of the second train = 190m.
The answer is 190
Choice C is the correct answer.
CAT 2021 Quant Question
A. 4
B. 3
C. 1
D. 2
Answer
The sequence is going on steps of 5.
Hence, the answer is 2
Choice D is the correct answer.
CAT 2021 Quant Question
The number of ways of distributing 15 identical balloons, 6 identical pencils and 3 identical erasers among 3 children, such that each child gets at least four balloons and one pencil, is
Answer:
Given that, there are 15 identical balloons, 6 identical pencils, and 3 identical erasers.
We need to distribute these items among 3 children, such that each child gets at least four balloons and one pencil.
So, every person gets four balloons and one pencil. After distribution, we have 3 balloons, 3 pencils, and 3 erasers remaining.
So, let’s first arrange the balloons in all possible combinations.
(3, 0, 0) , (2, 1, 0) , (1, 1, 1)
We can arrange (3, 0, 0) in three ways.
We can arrange (2, 1, 0) in six ways.
We can arrange (1, 1, 1) in only one way.
So, we can arrange balloons among three children in 10 ways.
Likewise, we can also arrange 3 pencils in 10 ways and 3 erasers in 10 ways.
Therefore, the total number of ways is 10 x 10 x 10 = 1000 ways
Hence, the answer is '1000’
CAT 2021 Quant Question
Answer:
Hence, the answer is ‘5’
CAT 2021 Quant Question
Consider the pair of equations: 
If x > y, then x - y equals
A. 8
B. 6
C. 7
D. 4
Answer
If we add these two equations,we get
(x - y) (x - y - 1) = 56
If we take x - y = n, then we will boil down to n (n - 1) = 56
Therefore, x - y = 8
Hence, the answer is 8
Choice A is the correct answer.
CAT 2021 Quant Question
From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, is
Answer
Let’s assume the capacity of the container is ‘c’
Let’s track down the milk which is retained.
The milk retained after taking first 9 litres from the container is 
The milk retained after taking next 9 litres from the container is 
The volumes of milk and water in the container are now in the ratio of 16 : 9.
The milk in the container is 
c = 45
The answer is 45
CAT 2021 Quant Question
Two trains A and B were moving in opposite directions, their speeds being in the ratio 5 : 3. The front end of A crossed the rear end of B 46 seconds after the front ends of the trains had crossed each other. It took another 69 seconds for the rear ends of the trains to cross each other. The ratio of length of train A to that of train B is
A. 2 : 3
B. 2 : 1
C. 5 : 3
D. 3 : 2
Answer:
Two trains A and B were moving in opposite directions, their speeds being in the ratio of 5 : 3.
The speed of train A is 5x.
The speed of train B is 3x.
Let’s assume length of train A and train B are 
The front end of A crossed the rear end of B 46 seconds after the front ends of the trains had crossed each other.
So, the distance travelled is 
For this, the time taken is 46 sec.
Trains took another 69 seconds for the rear ends of the trains to cross each other.
So, the distance travelled is 
For this, the time taken is 69 sec.
The relative speed is (5x + 3x), since they are moving opposite to each other.
The answer is '3 : 2’
Choice D is the correct answer.
CAT 2021 Quant Question
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 ₹ 21000 for the job, then the share of Charu, in INR, proportionate to the work done by him, is
A. 9000
B. 9100
C. 9200
D. 9150
Answer:
Anil can paint a house in 60 days. So, he can do 
of work per day.
Bimal can paint it in 84 days. So, he can do 
of work per day.
Let’s assume charu can paint it in ‘c’ days. So, he can do 
of work per day.
Anil alone does the work for 10 days. So, the work completed is 
The remaining work is 
After that, for 14 days they worked together.
Charu does his work for 14 days. So, the total work done by charu is 
The amount earned by charu = 
x 21000 = Rs 9100
The answer is '9100’
Choice B is the correct answer.
In what proportion can we mix rice of three varieties priced at Rs 20/kg , Rs 24/kg and Rs 36/kg so that price of mixture is Rs 28 ?
a) 3:4:5
b) 2:2:5
c) 1:3:4
d) 2:3:4
Way to solve other than using the options?