Percentage problems
- 1. 72% of the students of a certain class took Biology and 44% took Mathematics. If each student took Biology or Mathematics and 40 took both. The total number of students in the class was?
Options- A. 200
- B. 240
- C. 250
- D. 320 Discuss
Correct Answer: 250
Explanation:
Let the total number of students be 100
Then, n(A ? B) = n(A) + n(B) - n(A ? B) = (72 + 44 - 100)% = 16%
Now,16% of N = 40
? (16 x N) / 100 = 40
? N = (100 x 40) / 16 = 250
- 2. If the side of a square is increased by 30%, its area is increased by?
Options- A. 9%
- B. 30%
- C. 60%
- D. 69% Discuss
Correct Answer: 69%
Explanation:
Let side of square = 100 cm
Area = (100 x 100)cm2 = 10000 cm2
New area = (130 x 130)cm2 = 16900 cm2
Increase in area = (6900 / 10000) x 100% = 69%
- 3. The radius of circle is increased by 1%. What is the increased percent in its area?
Options- A. 1%
- B. 1.1 %
- C. 2%
- D. 2.01 % Discuss
Correct Answer: 2.01 %
Explanation:
Let radius of circle = 100 m
New radius = 101 m
original area = [? x (100)2 ]m2
New area = [? x (101)2 ]m2
Increase% = [? x {(101)2 - (100)2} / { ? x (100)2} ] x 100 %
= 201 / 100% = 2.01%
- 4. The length and breadth of square are increased by 30% and 20% respectively. The area of the rectangle so formed exceeds the area of the square by?
Options- A. 20%
- B. 36%
- C. 50%
- D. 56% Discuss
Correct Answer: 56%
Explanation:
Let length of square = 100 m and breadth of square = 100 m
Area = (100 x 100) m2 = 10000 m2
New length = 130 m and breadth = 120 m
New area of rectangle = (130 x 120) m2 = 15600 m2
Increase % = (5600 / 10000) x 100 % = 56%
- 5. The length of a rectangle is increased by 60%. By what per cent would the width have to be decreased to maintain the same area?
Options- A. 371/2%
- B. 60%
- C. 75%
- D. None of these Discuss
Correct Answer: 371/2%
Explanation:
Let length of a rectangle = 100 m,
Breadth = 100 m
New length = 160 m,
New breadth = B meters
Then, 160 x B = 100 x 100
? B = (100 x 100) / 160 = 125/2
Decrease in breadth = (100 - 125/2)% = 371/2%
- 6. The price of coffee is increased by 15% and a house wife reduced her consumption of coffee by 15% and hence her expenditure on coffee?
Options- A. Remains unchanged
- B. Increased by 4%
- C. Decreased by 4%
- D. Decreased by 2.25% Discuss
Correct Answer: Decreased by 2.25%
Explanation:
Consumption Decreases = (common %)2/100
= 225/100
= 2.25%.
- 7. In vocational course in a college 15% seats increase annually. If there were 800 students in 1992, how many student will be there in 1994?
Options- A. 920
- B. 1040
- C. 1058
- D. 1178 Discuss
Correct Answer: 1058
Explanation:
Required number = 800 x (1 + 15/100)2
= 800 x (23/20) x (23/20)
= 1058
- 8. A reduction of 21% in the price of wheat enables a person to buy 10.5 kg more for Rs. 100. What is the reduced price per kg?
Options- A. Rs. 2
- B. Rs. 2.25
- C. Rs. 30
- D. Rs. 2.50 Discuss
Correct Answer: Rs. 2
Explanation:
Let original rate = Rs. P per kg
New rate = 79% of Rs. P per kg
= Rs. (79 x P)/100) per kg
? {(100/79P)/100} - {100/P} = 10.5
? 10000/79P - 100/P = 10.5
? 10000 - 7900 = 10.5 x 79P
? P = 2100/(10.5 x 79)
? P = 2100/(10.5 x 79)
Reduced rate = Rs. (79/100) x 2100/(10.5 x 79) per kg = Rs. 2 per kg.
- 9. For a sphere of radius 10 cms. the numerical value of the surface area is how many per cent of the numerical value of its volume?
Options- A. 24%
- B. 26.5%
- C. 30%
- D. 45% Discuss
Correct Answer: 30%
Explanation:
Surface area sphere = 4? x (10)2
volume sphere=4?/3 x (10)3
= (4000?/3) cm3
? Required percentage = {(400? x 3) / (4000?)} x 100 %
= 30%
- 10. 5% income of A is equal to 15% income of B and 10% income of B is equal to 20% income of C. If income of C is Rs.2000, then total income of A, B and C is?
Options- A. Rs. 6000
- B. Rs. 18000
- C. Rs. 20000
- D. Rs. 14000 Discuss
Correct Answer: Rs. 18000
Explanation:
? 5% of A=15% of B and 10% of B = 20% of C
? A/20 = 3B/20 and B/10 = C/5
? B = 2C
? A/20 = (3/20) x 2C = 3C/10 =(3/10) x 2000 = 600
? A = (600 x 20) = 12000,
B = (2 x 2000) = 4000
? A + B + C = (12000 + 4000 + 2000) = 18000
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