CAT Previous Year Questions: Percentages (June 11) - CAT MCQ

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 = (3/2)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 = (0.34/1.1) x 100 = 31%

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%

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 = (68/100) x 150 = 102 students
⇒ Since the number of boys passed is 30,
⇒ Number of girls passed = 102 - 30 = 72
Total number of girls = (60/100) 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 = (18/90) x 100 = 20%

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

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 (5/4) = 80
C = 64
Now, we know that D scored 20% less than D
So, C = (4/5) x D
64 = (4/5) x D
D = 80 marks

Given Max. mark = N and Pass mark = 45% of N
A scores 36 marks and falls short of the pass mark by 68%
This means the pass mark must be reduced by (100 - 68)% = 32%
So, A scored 32% (45% N) = 36
N = 250 marks
The only option whose range falls within the obtained value is (B) 243 ≤ N ≤ 252

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.

Ravi invests 50% of his monthly savings in fixed deposits i.e from the remaining 50%, 30% percent of the rest of his savings = 15% is invested in stocks.
And the rest i.e 50 – 15 = 35% goes into Ravi's savings bank account.
If the total amount deposited by him in the bank (for savings account and fixed deposits) is Rs 59500
i.e. 50 + 35 = 85 % ⇒ 85% of total savings = 59500
We have to find the Ravi's total monthly savings (in Rs)
⇒  Total savings =
Ravi's total monthly savings is 70000 Rupees.

Given that the number of girls appearing for an admission test is twice the number of boys.
Let x be the number of boys and 2x be the number of girls.
We have to find the % of candidates who do not get admission if 30% of the girls and 45% of the boys get admission.
Those who got admission is 1.05x and those who do not get admission is 1.95x.
So, 
The percentage of candidates who do not get admission is 65%.

Given that in a shirt factory , 15% of the shirts produced are defective so 85% are non defective.
From this remaining 85% non defective shirts, 20% are sold in domestic market and the remaining 80% are left for export which is equal to 8840 shirts i.e. 80% of 85% of x = 8840

⇒ x = 13000
The number of shirts produced in the factory is 13000