Ratio Question Types
In this article, we are going to have a look at the various types of questions that are framed in aptitude examinations from the chapter of ratio.
Type 1
Q. Which of the following statements is correct?
(a) Two natural numbers whose sum is 64 cannot be in the ratio 13:3.
(b) Two natural numbers whose sum is 64 cannot be in the ratio 5:3.
(c) Two natural numbers whose sum is 64 cannot be in the ratio 3:2.
(d) Two natural numbers whose sum is 64 cannot be in the ratio 1:3.
Explanation:
For dividing 64 into two natural numbers, the sum of the terms of the ratio must be a factor of 64.
Only (3 + 2), i.e. 5 is not a factor of 64. So, two natural numbers whose sum is 64 cannot be in the ratio 3: 2.
Answer: (c)
Type 2: Using Ratio to find Average
Q. Ankur, Ben and Christopher charge Rs. 200, Rs. 150 and Rs. 180 per day respectively for their work. They work done by them is in the ratio of 3:2:4 respectively. What must be the average labour earning for all three workers per day?
(a) Rs. 160 (b) Rs. 175 (c) Rs. 200 (d) Rs. 180
Explanation:
Labour cost of Ankur = Rs. 200
Labour cost of Ben = Rs. 150
Labour cost of Christopher = Rs. 180
Ratio of the work of Ankur, Ben and Christopher = 3:2:4
So, let the work done by Ankur in one day = 3x units
The work done by Ben in one day = 2x units
The work done by Christopher in one day = 4x units
∴ The average labour earning of all the three workers per day = (200×3x + 150×2x + 180×4x)/(3x + 2x + 4x) = (600x + 300x + 720x)/9x = 1620x/9x = Rs. 180
Answer: (d)
Type 3: Adding/Subtracting to a ratio
Q. In an animal farm, the ratio of cows to pigs was 1:3. After 125 more cows were brought to the farm, the ratio of cows to pigs became 2:1. What is the total number of cows in the farm now?
(a) 75 (b) 100 (c) 150 (d) Cannot be determined
Explanations :
Let the original number of cows be x. Hence, the number of pigs = 3x.
After 125 more cows are brought to the farm, the ratio of cows to pigs = (x + 125) : 3x = 2 : 1
or (x + 125)/3x = 2/1
or x + 125 = 6x
or 5x = 125
or x = 25
Hence total number of cows in the farm now = x + 125 = 25 + 125 = 150
After 125 more cows, the ratio of cows to pigs changed from 1:3 to 2:1 (i.e. 6:3).
So, it essentially means 5 ratio units ≡ 125 (to change the ratio from 1:3 to 2:1)
or 1 ratio unit ≡ 25
So, the number of cows now = 6 ratio units = 150
Q. Two numbers are in the ratio 5:7. If 18 is added to first number and 20 is subtracted from the second number, the two numbers become equal. What must be the sum of these two numbers?
(a) 132 (b) 144 (c) 204 (d) 228
Explanations :
Two numbers are in the ratio 5:7. So, let the two numbers be 5x and 7x respectively.
If 18 is added to first number and 20 is subtracted from the second number, the two numbers become equal.
Hence, 5x + 18 = 7x – 20
or 2x = 38
or x = 19
Hence, the two numbers are 95 and 133
The sum of these two numbers = 95 + 133 = 228
Two numbers are in the ratio 5:7.
If 18 is added to first number and 20 is subtracted from the second number, the two numbers become equal, i.e. their ratio becomes 1:1, or 5:5, or 7:7.
So, it essentially means 7 - 5 = 2 ratio units ≡ 18 + 20 = 38
or 1 ratio unit ≡ 38/2 = 19
So, the sum of these two numbers = 5 × 19 + 7 × 19 = 12 × 19 = 228
Q. Aanya’s expenditure and savings are in the ratio 3:2. Her income increases by 10%, and her expenditure increases by 12%. By what percentage does her savings increase?
(a) 5% (b) 7% (c) 10% (d) 12%
Explanation:
Let Aanya’s expenditure and savings be Rs. 300 and Rs. 200 respectively. So, the income is Rs. 500.
Now, when income rises by 10% the income will become Rs. 550.
Similarly, the expenditure increases to Rs. 336 (300 + 12% of 300).
So, the new savings = Income - Expenditure = 550 - 336 = Rs. 214
Increase in savings = 214 - 200 = Rs. 14
∴ Percentage increase = (14/200) × 100 = 7%
Answer: (b)
Type 4: 3 people, 2 ratios
Q. Three friends A, B and C have an amount of Rs. 7,400 with them. The ratio of the amount that A has to what B has is 4:3. Similarly, the ratio of the amount that B has to what C has is 4:3 too. What must be the difference in the amounts that A and C hold?
(a) Rs. 1,200 (b) Rs. 1,400 (c) Rs. 1,600 (d) Rs. 1,800
Explanations :
Total amount = Rs. 7,400
Ratio of the amount with A to that with B = 4:3.
Similarly, the ratio of the amount with B to that with C = 4:3
Ratio of the amount with A to that with B can also be written as → 16 : 12
Ratio of the amount with B to that with C can also be written as → 12 : 9
So, the ratio of A, B and C = 16:12:9
Hence, 16x + 12x + 9x = 7400
or 37x = 7400
or x = 200
So, the amount of money with A = 16x = Rs. 3,200
The amount of money with C = 9x = Rs. 1,800
Difference between the amounts that A and C hold = 3200 – 1800 = Rs. 1,400
Total amount = Rs. 7,400
Ratio of the amount with A to that with B = 4:3.
Similarly, the ratio of the amount with B to that with C = 4:3
Ratio of the amount with A to that with B can also be written as → 16 : 12
Ratio of the amount with B to that with C can also be written as → 12 : 9
So, the ratio of A, B and C = 16:12:9
Total units = 16 + 12 + 9 = 37
Value per unit = Total amount / Total Unit = 7400/37 = Rs. 200
Difference between the amounts that A and C hold = 16 - 9 = 7 units = 7 × 200 = Rs. 1,400
Type 5: 4 people, 3 ratios
Q. Read the following information regarding the ages of 4 persons A, B, C, D and answer the item that follows:
- A is 2/5th the age of B.
- C is 3/4th the age of D.
- A is 5/3rd the age of C.
Who is the youngest of them?
(a) A (b) B (c) C (d) D
Explanation:
Let the ages of A, B, C and D be a, b, c and d.
So, a = (2/5) b
or a : b = 2:5 = 10:25
Similarly, c : d = 3:4 = 6:8
Now, a : c = 5:3 = 10:6
Thus, a : b : c : d = 10:25:6:8
We can see that, B is the eldest and C is the youngest of them all.
Answer: (c)