Ratio and Proportion MCQ Quiz - Objective Question with Answer for Ratio and Proportion - Download Free PDF
Last updated on Apr 21, 2025
Latest Ratio and Proportion MCQ Objective Questions
Ratio and Proportion Question 1:
A certain amount of money is divided between A, B and C in the ratio 8 : 4 : 3. If A divides his share between D and E in the ratio of 9 : 7, what will be the ratio of C's share to D's?
Answer (Detailed Solution Below)
Ratio and Proportion Question 1 Detailed Solution
Given:
The total amount is divided between A, B, and C in the ratio 8 : 4 : 3.
A divides his share between D and E in the ratio 9 : 7.
Formula used:
Profit = Time × Investment
Calculation:
Let the total amount of money be S.
A's share = (8 / (8 + 4 + 3)) × S = (8 / 15) × S
B's share = (4 / (8 + 4 + 3)) × S = (4 / 15) × S
C's share = (3 / (8 + 4 + 3)) × S = (3 / 15) × S
Now, A divides his share between D and E in the ratio 9 : 7.
So, D's share from A = (9 / (9 + 7)) × A's share = (9 / 16) × (8 / 15) × S
⇒ D's share = (72 / 240) × S = (3 / 10) × S
Now, we need to find the ratio of C's share to D's share:
C's share : D's share = (3 / 15) × S : (3 / 10) × S
⇒ Ratio = (3 / 15) × (10 / 3) = 2 / 3
∴ The ratio of C's share to D's share is 2 : 3.
Ratio and Proportion Question 2:
A certain sum of money was divided between x and y, in the ratio of 4 : 3. If y's share is ₹2,400, then the total initial capital is ___________.
Answer (Detailed Solution Below)
Ratio and Proportion Question 2 Detailed Solution
Given:
The sum of money is divided between x and y in the ratio 4:3.
y's share = ₹2,400
Calculation:
Let the total sum of money be S.
y's share = (3 / (4 + 3)) × S
y's share = (3 / 7) × S = ₹2,400
⇒ (3 / 7) × S = ₹2,400
⇒ S = ₹2,400 × (7 / 3)
⇒ S = ₹5,600
∴ The total initial capital is ₹5,600.
Ratio and Proportion Question 3:
What will be the third ratio of (a+b) and (a+b)2?
Answer (Detailed Solution Below)
Ratio and Proportion Question 3 Detailed Solution
Given:
We are asked to find the third ratio of (a + b) and (a + b)2.
Formula used:
Third proportion of a and b = b²/a
Calculation:
Third ratio = ((a + b)2)2/(a + b)
Third ratio = (a + b)4/(a + b)
We can simplify this expression:
Third ratio = (a + b)3
∴ The third ratio is (a + b)3.
Ratio and Proportion Question 4:
The monthly incomes of two friends Chetan and Vipul, are in the ratio 5 : 7 respectively and each of them saves ₹96000 every month. If the ratio of their monthly expenditure is 1 : 3, find the monthly income of Chetan(in ₹).
Answer (Detailed Solution Below)
Ratio and Proportion Question 4 Detailed Solution
Given:
Monthly incomes of Chetan and Vipul are in the ratio 5 : 7
Each of them saves ₹96000 every month
The ratio of their monthly expenditure is 1 : 3
Formula used:
Income = Expenditure + Savings
Calculation:
Let the monthly income of Chetan be 5x and that of Vipul be 7x.
Let the monthly expenditure of Chetan be y and that of Vipul be 3y (since the ratio of their expenditures is 1:3).
For Chetan, Income = Expenditure + Savings
5x = y + 96000
For Vipul, Income = Expenditure + Savings
7x = 3y + 96000
Now, solve the system of equations:
1) 5x = y + 96000
⇒ y = 5x - 96000
2) 7x = 3y + 96000
Substitute y = 5x - 96000 into equation 2:
7x = 3(5x - 96000) + 96000
7x = 15x - 288000 + 96000
7x = 15x - 192000
⇒ 7x - 15x = -192000
⇒ -8x = -192000
⇒ x = 24000
Now, the monthly income of Chetan = 5x = 5 × 24000 = ₹120000
∴ The monthly income of Chetan is ₹120000.
Ratio and Proportion Question 5:
If 19 , 57 , 81 , and y are in proportion, then the value of y is:
Answer (Detailed Solution Below)
Ratio and Proportion Question 5 Detailed Solution
Given:
19, 57, 81, and y are in proportion.
Formula Used:
If four numbers a, b, c, and d are in proportion, then a/b = c/d.
Calculation:
Here, a = 19, b = 57, c = 81, and d = y.
According to the formula:
⇒ 19 / 57 = 81 / y
Cross-multiplying:
⇒ 19y = 57 × 81
⇒ 19y = 4617
Dividing both sides by 19:
⇒ y = 4617 / 19
⇒ y = 243
The correct answer is option 4.
Top Ratio and Proportion MCQ Objective Questions
u : v = 4 : 7 and v : w = 9 : 7. If u = 72, then what is the value of w?
Answer (Detailed Solution Below)
Ratio and Proportion Question 6 Detailed Solution
Download Solution PDFGiven:
u : v = 4 : 7 and v : w = 9 : 7
Concept Used: In this type of question, number can be calculated by using the below formulae
Calculation:
u : v = 4 : 7 and v : w = 9 : 7
To make ratio v equal in both cases
We have to multiply the 1st ratio by 9 and 2nd ratio by 7
u : v = 9 × 4 : 9 × 7 = 36 : 63 ----(i)
v : w = 9 × 7 : 7 × 7 = 63 : 49 ----(ii)
Form (i) and (ii), we can see that the ratio v is equal in both cases
So, Equating the ratios we get,
u ∶ v ∶ w = 36 ∶ 63 ∶ 49
⇒ u ∶ w = 36 ∶ 49
When u = 72,
⇒ w = 49 × 72/36 = 98
∴ Value of w is 98
A bag has ₹ 785 in the denomination of ₹ 2, ₹ 5 and ₹ 10 coins. The coins are in the ratio of 6 : 9 : 10. How many coins of ₹ 5 are in the bag?
Answer (Detailed Solution Below)
Ratio and Proportion Question 7 Detailed Solution
Download Solution PDFGiven:
₹ 785 in the denomination of ₹ 2, ₹ 5 and ₹ 10 coins
The coins are in the ratio of 6 : 9 : 10
Calculation:
Let the number of coins of ₹ 2, ₹ 5 and ₹ 10 be 6x, 9x, and 10x respectively
⇒ (2 × 6x) + (5 × 9x) + (10 × 10x) = 785
⇒ 157x = 785
∴ x = 5
Number of coins of ₹ 5 = 9x = 9 × 5 = 45
∴ 45 coins of ₹ 5 are in the bag
If A : B = 7 : 8 and B : C = 7 : 9, then what is the ratio of A : B : C ?
Answer (Detailed Solution Below)
Ratio and Proportion Question 8 Detailed Solution
Download Solution PDFGiven:
A : B = 7 : 8
B : C = 7 : 9
Concept:
If N is divided into a : b, then
First part = N × a/(a + b)
Second part = N × b/(a + b)
Calculation:
A/B = 7/8 ----(i)
Also B/C = 7/9 ----(ii)
Multiply equation (i) and (ii) we get,
⇒ (A/B) × (B/C) = (7/8) × (7/9)
⇒ A/C = 49/72
∵ A : B = 49 : 56
∴ A : B : C = 49 : 56 : 72
Alternate Method
A : B = 7 : 8 = 49 : 56
B : C = 7 : 9 = 56 : 72
⇒ A : B : C = 49 : 56 : 72
A man has 25 paise, 50 paise and 1 Rupee coins. There are 220 coins in all and the total amount is 160. If there are thrice as many 1 Rupee coins as there are 25 paise coins, then what is the number of 50 paise coins?
Answer (Detailed Solution Below)
Ratio and Proportion Question 9 Detailed Solution
Download Solution PDFGiven:
Total coin = 220
Total money = Rs. 160
There are thrice as many 1 Rupee coins as there are 25 paise coins.
Concept used:
Ratio method is used.
Calculation:
Let the 25 paise coins be 'x'
So, one rupees coins = 3x
50 paise coins = 220 – x – (3x) = 220 – (4x)
According to the questions,
3x + [(220 – 4x)/2] + x/4 =160
⇒ (12x + 440 – 8x + x)/4 = 160
⇒ 5x + 440 = 640
⇒ 5x = 200
⇒ x = 40
So, 50 paise coins = 220 – (4x) = 220 – (4 × 40) = 60
∴ The number of 50 paise coin is 60.
If A is 25% less than B, then what will be the value of (2B - A)/A ?
Answer (Detailed Solution Below)
Ratio and Proportion Question 10 Detailed Solution
Download Solution PDFGiven:
A = 75% of B
Calculation:
A = 3/4 of B
⇒ A/B = 3/4
Let the value of A be 3x and B be 4x
So (2B – A)/A = (2 × 4x – 3x)/3x
⇒ (2B – A)/A = 5x/3x
∴ (2B – A)/A = 5/3
Short Trick:
Ratio of A : B = 3 : 4
∴ (2B – A)/A = (8 – 3) /3 = 5/3
If x : y = 5 : 4, then what will be the ratio of \(\left( {\frac{x}{y}} \right):\left( {\frac{y}{x}} \right)\)?
Answer (Detailed Solution Below)
Ratio and Proportion Question 11 Detailed Solution
Download Solution PDFGiven:
x : y = 5 : 4
Explanation:
(x/y) = (5/4)
(y/x) = (4/5)
Now, \(\left( {\frac{x}{y}} \right):\left( {\frac{y}{x}} \right)\) = (5/4)/(4/5) = 25/16
∴ \(\left( {\frac{x}{y}} \right):\left( {\frac{y}{x}} \right)\) = 25 : 16
How much should be added to each term of 4 : 7 so that it becomes 2 : 3?
Answer (Detailed Solution Below)
Ratio and Proportion Question 12 Detailed Solution
Download Solution PDFGiven :
Ratio of two numbers is 4 : 7
Calculations :
Let the number added to denominator and numerator be 'x'
Now according to the question
(4 + x)/(7 + x) = 2 : 3
⇒ 12 + 3x = 14 + 2x
⇒ x = 2
∴ 2 will be added to make the term in the ratio of 2 : 3.
The ratio of two numbers is 14 : 25. If the difference between them is 264, then which is the smaller of the two numbers?
Answer (Detailed Solution Below)
Ratio and Proportion Question 13 Detailed Solution
Download Solution PDFGiven:
Ratio of two numbers is 14 : 25
Difference between them is 264
Calculation:
Let the numbers be 14x and 25x
⇒ 25x – 14x = 264
⇒ 11x = 264
∴ x = 24
⇒ Smaller number = 14x = 14 × 24 = 336
∴ The smaller of the two numbers is 336.
The ratio of salaries of A and B is 6 ∶ 7 respectively. If B’s salary is increased by \(5\frac{1}{2}\%\), his total salary becomes Rs. 1,47,700. Find the salary of A (in Rs.).
Answer (Detailed Solution Below)
Ratio and Proportion Question 14 Detailed Solution
Download Solution PDFGiven:
Ratio of salaries of A and B = 6 : 7
B's salary increased by \(5\frac{1}{2}\%\)
Total salary of B = Rs. 147700
Calculation:
Let salary of A and B be Rs. 60x and Rs. 70x
Now,
Increased salary of B = 70x + 70x × \(5\frac{1}{2}\%\)
⇒ Rs. 73.85x
According to the question,
73.85x = 147700
⇒ x = 147700/73.85
⇒ x = 2000
So, actual salary of A = 60 × 2000
⇒ Rs. 120000
∴ The salary (in Rs.) of A is 120000.
If x : y = 6 : 5 and z : y = 9 : 25, then what is the ratio of x : z?
Answer (Detailed Solution Below)
Ratio and Proportion Question 15 Detailed Solution
Download Solution PDFGiven:
x : y = 6 : 5
And z : y = 9 : 25
Calculation :
x/y = 6/5 ---- (i)
And z/y = 9/25
⇒ y/z = 25/9 ---- (ii)
Multiply equation (i) and (ii) we get,
(x/y) × (y/z) = (6/5) × (25/9)
⇒ x/z = 10/3
∴ x : z = 10 : 3
Alternate Method
x : y = 6 : 5 ----- (i)
And z : y = 9 : 25 ---- (ii)
As y is in both the ratios, Multiply (i) × 5 to make equal value of y in both the ratios
x : y = (6 : 5) × 5 = 30 : 25 ---- (iii)
from (ii) and (iii), Since y is same in both the ratios
x : z = 30 : 9 = 10 : 3