Ratio and Proportion problems
- 1. On mixing two classes of students having average marks 25 and 40 respectively, the overall average obtained is 30 marks. Find the number of students in first class, if the second class has 30 students.?
Options- A. 45
- B. 60
- C. 70
- D. 80 Discuss
Correct Answer: 60
Explanation:
Students in the first class / Students in second class = (40 - 30)/(30 - 25) = 10/5 = 2/1
? Students in first class = 2 x 30 = 60
- 2. In a mixture of 60 L, the ratio of milk and water is 2 : 1. If the ratio of milk and water is to be 1 : 2, then the amount of water to be further added must be?
Options- A. 40 L
- B. 30 L
- C. 20 L
- D. 60 L Discuss
Correct Answer: 60 L
Explanation:
Milk = (2/3) x 60 = 40 L
Water = (1/3) x 60 = 20 L
Water added = W L
Now, 40/(20 + W) = 1/2
? W = 60 L
- 3. In a certain school, the ratio of boys to girls is 7 : 5. If there are 2400 students in the school, then how many girls are there in the school?
Options- A. 500
- B. 700
- C. 800
- D. 1000 Discuss
Correct Answer: 1000
Explanation:
Let the number of boys and girls are 7k and 5k, respectively.
Given, total number of students = 2400
? 7k + 5k = 2400
? 12k = 2400
? k = 200
? Required number of girls = 5k = 5 x 200 = 1000
- 4. If a + b : b + c : c + a = 6 : 7 : 8 and a + b + c = 14, then find c?
Options- A. 6
- B. 7
- C. 8
- D. 10 Discuss
Correct Answer: 10
Explanation:
Let a + b = 6k, b + c = 7k, c + a = 8k ...(i)
and a + b + c = 14 ...(ii)
From Eq. (i),
a + b + b + c + c + a = 6K + 7K + 8K
? 2(a + b + c) = 21K
? 2 x 14 = 21K
? K = 28/21 = 4/3
? a + b 6k = = 6 x 4/32 = 8
Subtracting Eq. (iii) from Eq. (ii), we get
(a + b + c) - (a + b) = 14 - 8 = 6
- 5. One - half of a certain number is equal to 65% of the 2nd number. Find the ratio of 1st to 2nd number.
Options- A. 10 : 13
- B. 8 : 13
- C. 13 : 8
- D. 13 : 10 Discuss
Correct Answer: 13 : 10
Explanation:
Let 1st number = x and 2nd number = y
According to the question 1/2 of x = 65% of y
? x/y = 130/100 = 13/10
? x : y = 13 : 10
- 6. The ratio between two number is 3 : 4. if each number is increased by 3, the ratio becomes 4 : 5. Find the differences between the numbers.
Options- A. 3
- B. 9
- C. 2
- D. 7 Discuss
Correct Answer: 3
Explanation:
Let the number be 3k and 4k.
According to the question,
(3k + 3)/(4k+ 3) = 4/5
? 5(3k + 3 ) = 4(4k + 3)
? 15k + 15 = 16k + 12
? k = 15 - 12 = 3
? Difference between the numbers = (4k - 3k) = k = 3
- 7. From each of two given numbers, half the smaller number is subtracted. After such subtraction, the larger number is 4 times as large as the smaller number. What is the ratio of the numbers?
Options- A. 5 : 2
- B. 1 : 4
- C. 4 : 1
- D. 4 : 5 Discuss
Correct Answer: 5 : 2
Explanation:
Let the smaller number = M and the greater number = N
According to the question ,
(N - M/2) = 4(M - M/2)
? N - M/2 = 4M/2
? N = 2M + M/2
? N = 5M/2
? N : M = 5 : 2
- 8. Two number are in the ratio of 2 : 3. If 9 is added to each number, they will be in the ratio 3 : 4. What is the product of the two numbers?
Options- A. 360
- B. 480
- C. 486
- D. 512 Discuss
Correct Answer: 486
Explanation:
Let the number be M and N
According to the question.
M/N = 2/3
? 3M = 2N
? 3M - 2N = 0 ...(i)
And (M + 9)/(N + 9) = 3/4
? 4M + 36 = 3N + 27
? 4M - 3N = -9 ...(ii)
Multiplying Ex. (i) by 4 and Eq. (ii) by 3 and subtracting, we get N = 27
Now, putting N = 27 in Eq. (i), we get 3M = 54
? M = 18
? Product of the given numbers = 27 x 18 = 486
- 9. Weekly income of two persons are in the ratio of 7 : 3 and their weekly expenses are in the ratio of 5 : 2. If each of them saves ? 300 per week, then the weekly income of the first person is?
Options- A. ? 7500
- B. ? 4500
- C. ? 6300
- D. ? 5400 Discuss
Correct Answer: ? 6300
Explanation:
Let the income of two persons are 7k and 3k
Expenditure of first person = 7k - 300
Expenditure of second person = 3k - 300
According to the question,
(7k - 300)/(3k - 300) = 5/2
? 14k - 600 = 15k - 1500
? k = 900
Income of first person = 7k = 7 x 900
= ? 6300
- 10. Amit and Sudesh have invested in the ratio of 4 : 7. If both invested a total amount of ? 49500, then find the investment of Sudesh?
Options- A. ? 31500
- B. ? 1800
- C. ? 31000
- D. ? 18500 Discuss
Correct Answer: ? 31500
Explanation:
Given total amount = ? 49500
Let part of Amit's investment = 4k
and part of sudesh's investment = 7k
According to the question
4k + 7k = 49500
? 11k = 49500
? k = 49500/11
? k = 4500
Hence investment of sudesh = 7k = 7 x 4500 = 31500
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