Ratio and Proportion MCQs for Competitive Examination
Solve the following problems.
Q. 41
If (x³ – y³) : (x² + xy + y²) = 5 : 1 and (x² – y²) : (x – y) = 7 : 1, then the ratio 2x : 3y equals
(A) 4 : 1
(B) 2 : 3
(C) 4 : 3
(D) 3 : 2
Answer: (A) 4 : 1
Explanation: N/A
Q. 42
If A : B = 2 : 3 and B : C = 3 : 7, then (A + B) : (B + C) : (C + A) is
(A) 4 : 8 : 9
(B) 5 : 8 : 9
(C) 5 : 10 : 9
(D) 4 : 10 : 9
Answer: (C) 5 : 10 : 9
Explanation: N/A
Q. 43
If (a + b) : √(ab) =4 : 1, where a > b > 0, then a : b is
(A) (2 + √3) : (2 – √3)
(B) (2 – √3) : (2 + √3)
(C) (3 + √2) : (3 – √2)
(D) (3 – √2) : (3 + √2)
Answer: (A) (2 + √3) : (2 – √3)
Explanation: (a + b)/4 = √(ab)/1
a + b = 4, √(ab) = 1 or ab = 1
Now, (a – b)² = (a + b)² – 4ab = 16 – 4 = 12
a – b = 2√3, Now, a = 2 + √3 and b = 2 – √3
and a : b = (2 + √3) : (2 – √3)
Q. 44
If (a + b) : (b + c) : (c + a) = 6 : 7 : 8 and (a + b + c) = 14, then the value of c is
(A) 6
(B) 7
(C) 8
(D) 14
Answer: (A) 6
Explanation: N/A
Q. 45
If x runs are scored by A, then y runs by B and z runs by C, then x : y = y : z = 3 : 2. If the total number of runs scored by A, B and C is 342, the runs scored by each would be respectively
(A) 144, 96, 64
(B) 162, 108, 72
(C) 180, 120, 80
(D) 189, 126, 84
Answer: (B) 162, 108, 72
Explanation: N/A
Q. 46
The ratio of 252.5 : 5³ is same as
(A) 5 : 3
(B) 5 : 6
(C) 1 : 25
(D) 25 : 1
Answer: (D) 25 : 1
Explanation: N/A
Q. 47
On mixing two sections of students from A and B having average marks 25 and 40 respectively, the overall average obtained is 30. Find the ratio of the students in the class A and B.
(A) 2 : 1
(B) 5 : 8
(C) 5 : 6
(D) 3 : 4
Answer: (A) 2 : 1
Explanation: N/A
Q. 48
94 is divided into two parts in such a way that the fifth part of the first and the eighth part of the second are in the ratio 3 : 4. The first part is
(A) 30
(B) 36
(C) 40
(D) 28
Answer: (A) 30
Explanation: N/A
Q. 49
If a : b : c = 7 : 3 : 5, then (a + b + c) : (2a + b − c) is equal to
(A) 1 : 2
(B) 2 : 3
(C) 3 : 4
(D) 5 : 4
Answer: (D) 5 : 4
Explanation: N/A
Q. 50
If a : b = c : d, then (ma + nc) : (mb + nd) is equal to
(A) m : n
(B) a : b
(C) (a + c)/(b + d)
(D) md : nc
Answer: (B) a : b
Explanation: N/A
Q. 51
If a : b = c : d = e : f = 1 : 2, then (3a + 5c + 7e) : (3b + 5d + 7f) is equal to
(A) 8 : 7
(B) 2 : 1
(C) 1 : 4
(D) 1 : 2
Answer: (D) 1 : 2
Explanation: N/A
Q. 52
A milkman makes 20% profit by selling milk mixed with water at Rs 9 per litre. If the cost price of 1 litre pure milk is Rs 10, then the ratio of milk and water in the mixture is
(A) 3 : 1
(B) 4 : 1
(C) 3 : 2
(D) 4 : 3
Answer: (A) 3 : 1
Explanation: N/A
Q. 53
My grandfather was 9 times older than me 16 years ago. He will be 3 times of my age 8 years from now. Eight years ago, the ratio of my age to that of my grandfather was
(A) 3 : 8
(B) 2 : 5
(C) 1 : 2
(D) 1 : 5
Answer: (D) 1 : 5
Explanation: N/A
Q. 54
The sum of the age of a father and his son is 100 years now. 5 years ago their age were in the ratio of 2 : 1. The ratio of the age of father and son after 10 years will be
(A) 5 : 3
(B) 4 : 3
(C) 10 : 7
(D) 3 : 5
Answer: (A) 5 : 3
Explanation: N/A
Q. 55
Harsha is 40 years old and Ritu is 60 years old. How many years ago was the ratio of their ages 3 : 5?
(A) 10 years
(B) 20 years
(C) 37 years
(D) 5 years
Answer: (A) 10 years
Explanation: N/A
Q. 56
If A and B are in the ratio 4 : 5 and the difference of their squares is 81, what is the value of A?
(A) 45
(B) 12
(C) 36
(D) 15
Answer: (B) 12
Explanation: N/A
Q. 57
The ratio of the number of balls in bags x, y is 2 : 3. Five balls are taken from bag y and are dropped in bag x. The number of balls is equal in each bag now. The number of balls in each bag now is
(A) 45
(B) 20
(C) 30
(D) 25
Answer: (D) 25
Explanation: Number of balls in bag x = 2k and number of balls in bag y = 3k
According to question, 2k + 5 = 3k – 5
Solving we have, k = 10,
Hence the number of balls in each bag = (2 * 20 + 5) = 25
Q. 58
Which number when added to each of the numbers 6, 7, 15, 17 will make the resulting numbers proportional?
(A) 6
(B) 5
(C) 4
(D) 3
Answer: (D) 3
Explanation: N/A
Q. 59
The ratio of two numbers is 3 : 4 and their HCF is 15. Then the sum of the two numbers is
(A) 105
(B) 115
(C) 120
(D) 110
Answer: (A) 105
Explanation: N/A
Q. 60
Ram got twice as many marks in English as in Science. His total marks in English, Science and Maths are 180. If the ratio of his marks in English and Maths is 2 : 3, what is his mark in Science?
(A) 30
(B) 60
(C) 72
(D) 90
Answer: (A) 30
Explanation: N/A