Aptitude Questions on Ratio & Proportions
Review Ratio and Proportion Concepts
Q. 1 Two friends, A and B, have their ages in the ratio 5:7. Fast forward six years, and their ages will be in the ratio 3:4. Can you figure out A’s current age?
A) 30 years
B) 24 years
C) 20 years
D) 18 years
Check Solution
Ans: A) 30 years.
Let the current ages of A and B be 5x and 7x respectively.
After 6 years,$\frac{5x + 6}{7x + 6} = \frac{3}{4}$.
Cross-multiplying, 4(5x+6)=3(7x+6).
$20x + 24 = 21x + 18 \Rightarrow x = 6$.
So, A’s age = $5 \times 6 = 30$.
Q. 2 If the ratio of Anjana’s income to Baani’s income is 5:4 and the ratio of their expenditures is 3:2. If Anjana saves $2000 and Baani saves $1000, what’s the ratio of their savings respectively?
A) 5:4
B) 4:5
C) 3:2
D) 2:1
Check Solution
Ans: A) 5:4.
Let A’s income and B’s income be 5x and 4x , and their expenditures be 3y and 2y .
Savings = Income – Expenditure.
For A: 5x−3y=2000 , For B: 4x−2y=1000 .
Solving these, x=1000 , y=1000 .
Thus, 5x:4x=5:4.
Q. 3 Two numbers are in the ratio 3:5. When you subtract 9 from each, the ratio magically changes to 12:23. What are these numbers?
A) 45, 75
B) 36, 60
C) 33, 55
D) 54, 90
Check Solution
Ans: C) 33, 55.
Let the numbers be 3x and 5x.
After subtracting 9, $\frac{3x – 9}{5x – 9} = \frac{12}{23}$.
Cross-multiplying, 23(3x−9)=12(5x−9).
$69x – 207 = 60x – 108 \Rightarrow 9x = 99 \Rightarrow x = 11$.
The numbers are $3 \times 11 = 33$ and $5 \times 11 = 55$.
Q. 4 The ratio of two numbers is 3:5. Add 10 to each, and the new ratio changes to 5:7. Find the original numbers?
A) 15 and 25
B) 21 and 35
C) 18 and 30
D) 24 and 40
Check Solution
Ans: A) 15 and 25.
Let the numbers be 3x and 5x.
After increasing by 10, $\frac{3x + 10}{5x + 10} = \frac{5}{7}$.
Cross-multiplying, 7(3x+10)=5(5x+10) .
Expanding and solving, 21x+70=25x+50, so $4x = 20 \Rightarrow x = 5$.
Thus, the numbers are $3 \times 5 = 15$ and $5 \times 5 = 25$.
Q. 5 If Arya’s salary compared to Bhuvi’s salary is like 4 to 7. After a $4000 raise for both, their salary ratio shifts to 6:11. What was Arya’s original salary?
A) $16000
B) $12000
C) $10000
D) $14000
Check Solution
Ans: D) $14000.
Let A’s and B’s original salaries be 4x and 7x.
After the increase, $\frac{4x + 4000}{7x + 4000} = \frac{6}{11}$.
Cross-multiplying, 11(4x+4000)=6(7x+4000).
Expanding, 44x+44000=42x+24000, so $2x = 20000 \Rightarrow x = 10000$.
A’s original salary = $4 \times 10000 = 40000$.
Q. 6 Three numbers are in 2:3:5 ratio. Interestingly, the sum of the first and third exceeds the second by 16. Can you decode the numbers?
A) 8, 12, 20
B) 4, 6, 10
C) 12, 18, 30
D) 6, 9, 15
Check Solution
Ans: A) 8, 12, 20.
Let the numbers be 2x , 3x , and 5x .
According to the problem, $2x + 5x – 3x = 16 \Rightarrow 4x = 16 \Rightarrow x = 4$.
So, the numbers are $2 \times 4 = 8$, $3 \times 4 = 12$, and $5 \times 4 = 20$.
Q. 7 A bag of colorful balls contains red, blue, and green balls in a 3:4:5 ratio. If there are 60 green balls, how many balls are in the bag altogether?
A) 120
B) 144
C) 180
D) 150
Check Solution
Ans: B) 144.
Let the numbers of red, blue, and green balls be 3x, 4x, and 5x, respectively.
Since 5x=60, x=12.
Total number of balls = $3x + 4x + 5x = 12x = 12 \times 12 = 144$.
Q. 8 The incomes of A, B, and C are in the ratio 7:9:12, while their expenses are in the ratio 8:9:15. If their respective savings are $200, $150, and $300, what’s A’s income?
A) $1400
B) $2100
C) $2800
D) $3500
Check Solution
Ans: A) $1400.
Let A’s, B’s, and C’s incomes be 7x, 9x, and 12x, and their expenses be 8y, 9y, and 15y.
Since income – expense = savings, we get:
7x−8y=200, 9x−9y=150, and 12x−15y=300.
Solving these, we find x=200.
So, A’s income = $7 \times 200 = 1400$.
Q. 9 A and B’s present ages are tied at a ratio of 4:5. But if you rewind five years, their ages were in the ratio 3:4. Can you determine their present ages?
A) 20 and 25 years
B) 16 and 20 years
C) 24 and 30 years
D) 28 and 35 years
Check Solution
Ans: A) 20 and 25 years.
Let A’s age and B’s age be 4x and 5x respectively.
Five years ago, $\frac{4x – 5}{5x – 5} = \frac{3}{4}$.
Cross-multiplying, 4(4x−5)=3(5x−5).
This gives 16x−20=15x−15, so x=5.
Thus, A’s age = $4 \times 5 = 20$, B’s age = $5 \times 5 = 25$.
Q. 10 Two trains race with speed ratios of 5:8. The faster train covers 400 km in just 5 hours. What’s the speed of the slower train?
A) 40 km/hr
B) 50 km/hr
C) 60 km/hr
D) 80 km/hr
Check Solution
Ans: B) 50 km/hr.
Speed of the faster train = $\frac{400}{5} = 80$ km/hr.
Let the speed of the slower train be x. Then, $\frac{x}{80} = \frac{5}{8}$, so $x = 80 \times \frac{5}{8} = 50$ km/hr.
Q. 11 A chocolate manufacturer packs dark, milk, and white chocolates in a box in the ratio 4:5:6. If the manufacturer decides to add 12 more milk chocolates to the box, the new ratio becomes 4:6:6. How many chocolates were initially in the box?
A) 45
B) 180
C) 120
D) 135
Check Solution
Ans: B) 180
Let the total initial number of chocolates be 4x+5x+6x=15x
When 12 milk chocolates are added, the ratio changes: $\frac{4x}{5x+12} = \frac{4}{6}$
Cross-multiplying: 24x = 20x+48 ⟹ 4x=48 ⟹ x=12
Initial total chocolates = 15x=15×12=180
Q. 12 A farmer has cows and goats in the ratio 7:9. If 20 more cows are added to the farm, the ratio changes to 4:3. How many goats are currently on the farm?
A) 36
B) 54
C) 63
D) 72
Check Solution
Ans: A) 36
Let the number of cows and goats be 7x and 9x respectively
When 20 more cows are added, the new ratio is: (7x+20)/9x = 4/3
Cross-multiplying: 21x + 60= 36x ⟹ 15x = 60 ⟹ x=4
Number of goats =9×4 = 36
Q. 13 In a town, the ratio of people speaking English, Spanish, and French is 8:6:5. If the total population is 19,000, how many more people speak English than French?
A) 1000
B) 1500
C) 2000
D) 3000
Check Solution
Ans: D) 3000
The total ratio sum is 8+6+5=19
The value of one ratio unit = 19000/19 = 1000
Number of people speaking English = 8×1000 = 8000
Number of people speaking French = 5×1000=5000
Difference = 8000−5000=3000
Q. 14 A jar contains a mixture of juice and water in the ratio 5:3. If 16 litres of the mixture are replaced with water, the new ratio becomes 3:5. What is the initial volume of the mixture?
A) 24 litres
B) 32 litres
C) 40 litres
D) 48 litres
Check Solution
Ans: C) 40 litres
Let the initial volume of the mixture be 5x + 3x = 8x
When 16 litres are replaced, the juice and water volumes change:
Juice: 5x − 5/8×16
Water: 3x+16 − 3/8×16 = 3x + 10
The new ratio is: $\frac{5x – 10}{3x + 16 – 6} = \frac{3}{5}$
Cross-multiplying: $5*(5x−10) = 3*(3x+10) ⟹ 16x = 80 ⟹ x = 5$
Initial volume = 8x = 8×5 = 40
Practice Questions for next topic: https://www.learntheta.com/aptitude-questions-profit-loss-partnership/