CAT 2022 QA Slot-2 Question 1-
In an election, there were four candidates and 80% of the registered voters casted their votes. One of the candidates received 30% of the casted vote
while the other three candidates received the remaining casted votes in the proportion 1 : 2 : 3. If the winner of the election received 2512 votes more
than the candidate with the second highest votes, then the number of registered voters was:
(a) 60288
(b) 50240
(c) 40192
(d) 62800
Explanation
One candidate got 30% of the polled votes, the remaining three got in the ratio of 1 : 2 : 3
The polled votes were split in 3 : 7 ratio.
The 70% of them were again split in the ratio 1 : 2 : 3
The votes were polled in the ratio of 6(3) : 7(1 : 2 : 3)
18 : 7 : 14 : 21
Let’s assume that the actual polled votes are 18x, 7x, 14x, 21x
The winner of the election received 2512 votes more than the candidate with the second highest votes.
21x – 18x = 2512
3x = 2512
Total polled votes = 18x + 7x + 14x + 21x = 60x = 20(3x) = 20(2512) = 50,240
The polled votes represent 80% of the total registered votes.
Total registered votes = 50,240 + 12,560 = 62,800.
CAT QA 2021 Slot-2 Question 2-
Raj invested ₹ 10000 in a fund. At the end of first year, he incurred a loss but his balance was more than ₹ 5000. This balance, when invested for another year, grew and the percentage of growth in the second year was five times the percentage of loss in the first year. If the gain of Raj from the initial investment over the two year period is 35%, then the percentage of loss in the first year is
A.15
B. 5
C.10
D.70
Explanation
Let the total investment be P, then at the end of the first year, after a loss of x percentage the value of the investment becomes
P(1 – x)
Then in the next year the value of the investment increases by 5x
So, the overall value of the investment becomes
P(1 – x)(1 + 5x)
This is an increase of 35% from the initial investment amount.
Hence,
1.35 P = P (1 – x)(1 + 5x)
Going by the options we can see that the equation is satisfied when x = 10
Hence 10 is the answer
CAT QA 2021 Slot-3 Question 3- In a tournament, a team has played 40 matches so far and won 30% of them. If they win 60% of the remaining matches, their overall win percentage will be 50%. Suppose they win 90% of the remaining matches, then the total number of matches won by the team in the tournament will be
A. 86
B .84
C .78
D .80
Explanation
Let the number of matches to be played be ‘x’
We are given that 40 matches are already played and 30% of them are won.
If 60% of the remaining matches are won, then the overall win percentage is 50%.
30% of 40 + 60% of x = 50% of (40 + x)
0.3 (40) + 0.6 (x) = 0.5 (40 + x)
12 + 0.6 (x) = 20 + 0.5 (x)
0.1 (x) = 8
x = 80
The number of matches to be played is 80.
If the team wins 90% of the remaining matches, it would win 90% of 80 = 72 matches.
Total matches won by the team
= 30% of 40 + 72
= 12 + 72 = 84
CAT QA 2021 Slot- 3 Question 4-
The total of male and female populations in a city increased by 25% from 1970 to 1980. During the same
period, the male population increased by 40% while the female population increased by 20%. From 1980 to
1990, the female population increased by 25%. In 1990, if the female population is twice the male
population, then the percentage increase in the total of male and female populations in the city from 1970
to 1990 is
A 68.25
B 68.75
C 68.50
D 69.25
Explanation
From 1970 to 1980,
the male population increased by 40%
the female population increased by 20%
the overall population increased by 25%
Population of 1970 and 1980
1.4M + 1.2F = 1.25(M + F)
1.4M + 1.2F = 1.25M + 1.25F
1.4M – 1.25M = 1.25F – 1.2F
0.15M = 0.05F
F = 3M
From 1980 to 1990,
Female population increased by 25%
Therefore, the female population in 1990 = 1.25 × 1.2F = 1.5F
Since, the female population in 1990 is twice the male population,
Male population in 1990 = 1.5F ÷ 2 = 0.75F
Since F = 3M,
Male population in 1990 = 2.25M
Total population in 1970 = M + F = M + 3M = 4M
Total population in 1990 = 2.25M + 1.5F = 2.25M + 4.5M = 6.75M
The percentage increase in population = 6.75M−4M4M×100
= 2.754×100
= 68.75%
CAT 2022 Slot 3 – Question 5-
Nitu has an initial capital of ₹20,000
. Out of this, she invests ₹8,000
at 5.5%
in bank A,₹5,000
at 5.6%
in bank B
and the remaining amount at x%
in bank C
, each rate being simple interest per annum. Her combined annual interest income from these investments is equal to 5%
of the initial capital. If she had invested her entire initial capital in bank C alone, then her annual interest income, in rupees, would have been
A.900
B.700
C.1000
D.800
Explanation
If Neetu intended to get a 5% annual interest, ideally all the banks should have maintained a 5% interest rate.
But Bank A returns 0.5% extra interest on 8000 rupees, which is 40 rupees.
But Bank B returns 0.6% extra interest on 5000 rupees, which is 30 rupees.
A & B combines are paying 70 rupees extra than 5%.
So Bank C should maintain such an interest rate that, the interest generated on the remaining 7000 rupees is 70 less than 5% interest.
Since 70 is 1% of 7000. The interest rate at Bank C should be 5% – 1% = 4%
If all the 20,000 rupees were invested in Bank C, the interest generated is 4% of 20,000 = 800 rupees.
CAT 2022 Slot 2 – Question 6- Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is
Explanation
CAT 2020 Slot 2 Question 7-
In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent 150 more due to price increase of rice and wheat by 20% and 12%, respectively. If John had spent 450 on rice in April, then how much did he spend on wheat in May?
A.590
B.580
C.560
D.570
Explanation
Rice in april = 450
Increase in 20% = +90
Since 150 more is the amount he spent, +60 should be on wheat
So 12%(Wheat) = Rs 60
Price of wheat = 500
So +60 in may = 500 + 60 = 560
CAT 2020 Slot 1 Question 8-
In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates, and 25% of the literates are young, then the percentage of old people among the illiterates is nearest to
A.59
B.62
C.66
D.55
Explanation
In a group 28% are young, 72% are old
In the same group 65% are literates and 35% are illiterates
Young literates = 14
(65%) = 16.25%, So remaining 11.75% are young illiterates
Out of 35% illiterates = 11.75% is young and remaining 23.25% are old illiterates
So, 23.2535
× 100 ≅ 66
CAT 2019 Slot 2 Question 9- In 2010, a library contained a total of 11500 books in two categories – fiction and non-fiction. In 2015, the library contained a total of 12760 books in these two categories. During this period, there was 10% increase in the fiction category while there was 12% increase in the non-fiction category. How many fiction books were in the library in 2015?
A.6600
B.6160
C.6000
D.5500
Explanation
Increase in books = 12760 – 11500 = 1260
+ x (11500 – x) = 1260
10x + 12 x 11500 – 12x = 126000
x = 6000 books
So, Fiction books in 2015, 6000 + 600 = 6600 books
CAT 2019 Slot 2 Question 10- In an examination, the score of A was 10% less than that of B, the score of B was 25% more than that of C, and the score of C was 20% less than that of D. If A scored 72, then the score of D was
Explanation
From the data,
A scored 72
A’s score was 10% less than B
So, Score of B = 80
We know that B was 25% more than C
So, C x = 80
C = 64
Now, we know that D scored 20% less than D
So, C = x D
64 = x D
D = 80 marks
CAT 2019 Slot 1 Question 11-
In a class, 60% of the students are girls and the rest are boys. There are 30 more girls than boys. If 68% of the students, including 30 boys,pass an examination, the percentage of the girls who do not pass is
Explanation
Given that there are 60 % girls and 40 % boys
It is also given that there are 30 more girls than boys.
So, (60 % – 40 %) of total class strength = 30 students
=> 20 % of total class strength = 30 students
=> Total class strength = 30 x 5 = 150 students
It is also given that 68% of students pass the the examination, which includes 30 boys
So, Number of students passed = 68% of Total students
=> Number of students passed = x 150 = 102 students
=> Since the number of boys passed is 30,
=> Number of girls passed = 102 – 30 = 72
Total number of girls = x 150 = 90
Total number of girls = Girls who passed + Girls who did not pass
Girls who did not pass = 90 – 72 = 18
Percentage of girls who did not pass = x 100 = 20 %
CAT 2019 Slot 1 Question 12-
Meena scores 40% in an examination and after review, even though her score is increased by 50%, she fails by 35 marks. If her post-review score is increased by 20%, she will have 7 marks more than the passing score. The percentage score needed for passing the examination is
A.75
B.80
C.60
D.70
Explanation
Meena scores 40 % in an exam
After review, she scores 50 % more => Increase of 50 % from 40 % = 40% + 20% = 60%
She fails by 35 marks, by scoring 60%
60% score = Pass mark – 35 —– (1)
If her post review score is increased by 20%, she would have 7 more than the pass mark.
20% of 60% = 12 %
So, 60% + 12% = 72% of marks = Pass mark + 7 —— (2)
So, 12% marks = 35 + 7 (5: 1 ratio)
So, similarly 12% can be re written as 10 % and 2 % (maintaining the 5:1 ratio)
Hence the pass percentage = 60 % + 10 % = 70%
(or)
Pass percentage = 72 % – 2 % = 70%
CAT 2019 Slot 1 Question 13-
The income of Amala is 20% more than that of Bimala and 20% less than that of Kamala. If Kamala’s income goes down by 4% and Bimala’s goes up by 10%, then the percentage by which Kamala’s income would exceed Bimala’s is nearest to
A.28
B.29
C.31
D.32
Explanation
Let Bimala’s income be B. Amala’s income is 20% more than B.
So, A = 1.2 B
Similarly, Amala’s income is 20% less than that of Kamala.
A= 0.8K
Therefore, 1.2B = 0.8K (or) K = B
Now, Bimala’s new income goes up by 10% = 1.1B
Kamala’s income goes down by 4%
4% (1.5B) = 0.06B
Therefore, Kamala’s new income is = 1.5B – 0.06B = 1.44B
So, K = 1.44B and B = 1.1 B
Percentage change = 0.34 B = x 100 = 31%
CAT 2017 Slot 2 Question 14-
In a village, the production of food grains increased by 40% and the per capita production of food grains increased by 27% during a certain period. The percentage by which the population of the village increased during the same period is nearest to
A.16
B.13
C.10
D.7
Explanation
Given that the production of food grains increased by 40%.
Let initial production be y and after increase it becomes 1.4x
Per capita production of food grains increased by 27%.
Per capita income = productionoffoodgrains/no.ofpeople
⟹ let the initial Per capita income be xy
.
After increase it becomes 1.27[xy
].
CAT 2017 Question Paper Quants Slot 2 Percentages
⟹ 1.4x?
= 1.27[xy
]
⟹ ? = 1.4/1.27
× y = 1.1y
Hence there is an increase of 10% in the population of the village.
CAT 2017 Slot 1 – Question 15- Arun’s present age in years is 40% of Barun’s. In another few years, Arun’s age will be half of Barun’s. By what percentage will Barun’s age increase during this period?
Explanation
Given that Arun’s present age in years is 40% of Barun’s. And after few years, Arun’s age will be half of Barun’s. We have to find by what percentage will Barun’s age increase during this period.
So Arun’s present age is 2x and Barun’s present age will be equal to 5x.
2(2x + y) = 5x + y
4x + 2y = 5x + y
4x + 2y = 5x + y
y = x
So 2x and 5x becomes 3x and 6x respectively.
By what percentage will Barun’s age increase during this period is that x increases of 5x so it increases by 20%.
Hence 20% of Barun’s age will increase during this period.
Hence, the answer is 20
