# Ratio Proportion

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## Practice Questions - Ratio Proportion

Q1) The ratio between two numbers is 4:5 and their sum is 630. Find the numbers.
1) 210, 280
2) 280, 350
3) 210, 420
4) 180, 450

Solution:

First Number = (4/9)×630 = 280
Second Number = (5/9)×630 = 350
Hence, option 2.

Q2) Find the mean proportion of 4 and 36.
1) 8
2) 16
3) 20
4) 12

Solution:

Mean proportion of 4 and 36 = √4×36 = 12
Hence, option 4.

Q3) Find the third proportion of 16 and 24.
1) 36
2) 24
3) 18
4) 30

Solution:

Let P be the third proportion
16:24 = 24:P
On solving, P = 36
Hence, option 1.

Q4) Two numbers are in the ratio of 4:5. If 5 is subtracted from each, then they are in the ratio of 3:4. Find the first number?
1) 15
2) 12
3) 20
4) 25

Solution:

Let two numbers be 4k, 5k.
A.T.Q.

On solving, k = 5
First number is 4(5) = 20
Hence, option 3.

### Download: Practice Questions on Ratio Proportion

Q5) If a:b = 2:3 then (3a + 2b):(3a + 4b) is equal to
1) 3:2
2) 4:3
3) 3:4
4) 2:3

Solution:

As a:b = 2:3
a = 2k, b = 3k
(3a + 2b):(3a + 4b) = (12k):(18k) = 2:3
Hence, option 4.

Q6) Find the number which when added to the terms of the ratio 13:28 makes it equal to the ratio 1:2.
1) 4
2) 3
3) 2
4) 1

Solution:

(13 + x)/(28 + x) = 1/2
x = 2
Hence, option 3.

Q7) A bag contains rupee, 50-paise and 25-paise coins in the ratio 5:7:9. If the total amount in the bag is Rs 430, find the number of coins of each kind.
1) 360, 280, 200
2) 200, 360, 280
3) 280, 360, 200
4) 200, 280, 360

Solution:

Number of 1 rupee coins = 5k
Number of 50-paise coins = 7k
Number of 25-paise coins = 9k
1 × 5k + 0.5 × 7k + 0.25 × 9k = 430
k = 40
Number of coins of each kind = 5k, 7k, 9k = 200, 280, 360
Hence, option 4.

Q8) Sum of three numbers is 275. If the ratio between the first and second be 3:7 and that between the second and third be 2:5, then find the second number.
1) 30
2) 175
3) 70
4) 80

Solution:

a + b + c = 275
a/b = 3/7 = 6/14
b/c = 2/5 = 14/35
a : b : c = 6 : 14 : 35
b = (14/55)×275 = 70
Hence, option 3.

### Download: Practice Questions on Ratios and Mixtures

Q9) The income of A and B are in the ratio 9:4 and their expenses are in the ratio 7:3. If each of them saves Rs 2000, what are their incomes?
1) 90000, 40000
2) 72000, 32000
3) 72000, 16000
4) 27000, 12000

Solution:

Income of A (Ia) = 9x
Income of B (Ib) = 4x
Expense of A (Ea) = 7y
Expense of B (Eb) = 3y
9x - 7y = 2000
4x - 3y = 2000
On solving, x = 8000, y = 10000
Income of A (Ia) = 9x = 9(8000) = Rs 72000
Income of B (Ib) = 4x = 4(8000) = Rs 32000
Hence, option 2.

Q10) A cat takes 5 leaps for every 4 leaps of a dog but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?
1) 11:15
2) 15:11
3) 16:15
4) 15:16

Solution:

4 leaps of the cat = 3 leaps of the dog
1 leap of the cat = 3/4 leaps of the dog
cat takes 5 leaps for every 4 leaps of a dog i.e. 5 leaps of the cat : 4 leaps of the dog
5×3/4 leaps of the dog : 4 leaps of the dog = 15/4 : 4 = 15:16
Hence, option 4.