This set of Aptitude Questions and Answers (MCQs) focuses on “Increase or Decrease – Set 2”.
1. The height and length of a cuboid is increased by 50% and 15% respectively. Find the percentage increase in its volume.
a) 72%
b) 72.5%
c) 73%
d) 73.5%
View Answer
Explanation: Let the length, breadth and height of the cuboid be 10, 10 and 10, respectively.
Volume of the cuboid initially = 10 * 10 * 10 = 1,000 cubic units
Length of the new cuboid = 10 + 15% of 10 = 10 + 1.5 = 11.5
Height of the new cuboid = 10 + 50% of 10 = 10 + 5 = 15
Volume of the new cuboid = 15 * 11.5 * 10 = 1725
Change in volume = 1725 – 1000 = 725
Percentage change = 725 / 1000 * 100 = 72.5% increased
2. The sides of a square are increased by 72%. Find the percentage increase in its area.
a) 195.84%
b) 199.85%
c) 198.5%
d) 194.85%
View Answer
Explanation: Let the side of the square be 10.
The initial area of the square = 10 * 10 = 100
The change in sides = 72%
The change = 10 + 72% of 10 = 10 + 7.2 = 17.2
New area of the square = 17.2 * 17.2 = 295.84
Change in the area of the square = 295.84 – 100 = 195.84
Percentage change = 195.84 / 100 * 100 = 195.84%
3. The area of a rectangle is increased 43%. If the length of the rectangle is increased by 10% find the change in its breadth.
a) 20%
b) 25%
c) 30%
d) 50%
View Answer
Explanation: Let the initial length and breadth of the rectangle be 10 and 10, respectively.
The initial area of the square = 100
The changed area of the square = 100 + 43% of 100 = 100 + 43 = 143
The changed length of the rectangle = 10 + 10% of 10 = 10 + 1 = 11
Let the changed breadth of the square be x.
11 * x = 143
X = 143 / 11 = 13
Changed breadth = 13
Initial breadth = 10
Change = 3
Percentage change = 3 / 10 * 100 = 30%
4. The height of a triangle is increased by 33%. Find the change in the length of the base if the area of the triangle remains constant.
a) 11%
b) 12%
c) 13%
d) 15%
View Answer
Explanation: Let the initial base and height of the triangle be 10 and 10, respectively.
The initial area of the triangle = \(\frac {1}{2}\) * 10 * 10 = 50 square units
The increased height of the triangle = 10 + 33% of 10 = 10 + 3.3 = 13.3
The final area of the triangle is same as the initial area = 100 square units
Let the changed base of the triangle be x.
\(\frac {1}{2}\) * 13.3 * x = 100
X = 2 * 100 / 13.3 = 200 / 13.3 = 15.03 ≈ 15% decrease
5. A number is increased by 20% after every 10 days. Find the percentage change in value of the number after 40 days.
a) 105.36%
b) 107.36%
c) 109.56%
d) 111.56%
View Answer
Explanation: Let the value of the number be 100.
The value of the number after 10 days = 100 + 20% of 100 = 120
The value of the number after 20 days = 120 + 20% of 120 = 120 + 24 = 144
The value of the number after 30 days = 144 + 20% of 144 = 144 + 28.8 = 172.8
The value of the number after 40 days = 172.8 + 20% of 172.8 = 172.8 + 34.56 = 207.36
The difference between the initial value and the final value = 207.36 – 100 = 107.36
Percentage change = 107.36 / 100 * 100 = 107.36%
6. The height of a boy increases at a rate of 10% per annum. Find his height after 3 years if his height now is 3 feet.
a) 5 feet
b) 4.5 feet
c) 4 feet
d) 3.7 feet
View Answer
Explanation: The height of the boy after 1 year = 3 + 10% of 3 = 3 + 0.3 = 3.3 feet
The height of the boy after 2 years = 3.3 + 10% of 3.3 = 3.3 + 0.33 = 3.63 feet
The height of the boy after 3 years = 3.63 + 10% of 3.63 = 3.63 + 0.363 = 3.993 feet ≈ 4 feet
7. The average salary of a family is increased by 50% every year. If the expenditure of the family is 20% of the total income during the first year and is increased at a rate of 30% each year, find the ratio of income to expenses after 2 years.
a) 1125 : 169
b) 1169 : 125
c) 1215 : 169
d) 1150 : 169
View Answer
Explanation: Let the salary of the family during the first year be 100.
The expenses of the family in relation to the income during the first year = 20% of 100 = 20
The income of the family after a year = 100 + 50% of 100 = 150
The income of the family after 2 years = 150 + 50% of 150 = 150 + 75 = 225
The expenditure of the family during the first year = 20
The expenditure of the family after a year = 20 + 30% of 20 = 20 + 6 = 26
The expenditure of the family after 2 years = 26 + 30% of 26 = 26 + 7.8 = 33.8
The ratio of income to expenditure = 225 : 33.8 = 1125 : 169
8. Two numbers are increased at a rate of 20% and 30% per annum. If the numbers are in a ratio 8 : 9, find the ratio of the numbers after 2 years.
a) 129 : 168
b) 128 : 169
c) 147 : 169
d) 122 : 179
View Answer
Explanation: Let the numbers be 80 and 90, respectively.
The numbers after 1 year = 80 + 20% of 80, 90 + 30% of 90 = 80 + 16, 90 + 27 = 96, 117
The numbers after 2 years = 96 + 20% of 96, 117 + 30% of 117 = 96 + 19.2, 117 + 35.1 = 115.2, 152.1
The ratio of the numbers after 2 years = 1152 : 1521 = 128 : 169
9. The followers of an Instagram influencer increases at a rate of 10%, 20%, 60%, 20% and 25% for the first 5 days of a month. If the followers doubled after this during the entire month, find his total followers gain during the month.
a) 304%
b) 404%
c) 504%
d) 604%
View Answer
Explanation: Let his followers at the beginning of the months be 100.
His followers after first increment = 100 + 10% of 100 = 100 + 10 = 110
His followers after second increment = 110 + 20% of 110 = 110 + 22 = 132
His followers after the third increment = 132 + 60% of 132 = 132 + 79.2 = 201.2
His followers after the fourth increment = 201.2 + 20% of 201.2 = 201.2 + 40.42 = 241.62
His followers after the fifth increment = 241.62 + 25% of 241.62 = 241.62 + 60.405 = 302.025
His followers after the month = double of 302.025 = 604.05 ≈ 604
The change in his followers = 604 – 100 = 504
The percentage growth = 504 / 100 * 100 = 504%
10. A is 20% of a number a is b. What percentage of a is b?
a) 100%
b) 200%
c) 450%
d) 500%
View Answer
Explanation: Let the number a be 100.
A is 20% of b (given).
20% of a number is 100.
100% of the number = 100 / 20 * 100 = 500
The number b is 500 in terms of the assumption.
The percentage of a is b:
The percentage of 100 is 500 = 500 / 100 * 100 = 500%
500% of a is equal to b.
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