Ratio and Proportion Questions and Answers for Competitive Exams

Question 1

Hard

A box contains ₹1, 50-paise and 25-paise coins. The values of the coins of each kind are in the ratio 7 : 1 : 5. If there are 377 coins in all, how many 50-paise coins are there?

A 29 coins

B 26 coins

C 260 coins

D 52 coins

Correct Answer: B

Explanation:

Step 1: Let the values be ₹7v, ₹1v and ₹5v. Step 2: Number of coins = value ÷ face value: 7v ÷ 1 = 7v, 1v ÷ 0.5 = 2v, 5v ÷ 0.25 = 20v, so the numbers are in the ratio 7 : 2 : 20 = 7 : 2 : 20. Step 3: Total parts = 29; 1 part = 377 ÷ 29 = 13 → 50-paise coins = 2 × 13 = 26.

Question 2

Easy

Divide ₹1400 among A and B in the inverse ratio of 3 : 2. What is A's share?

A ₹840

B ₹280

C ₹1120

D ₹560

Correct Answer: D

Explanation:

Step 1: The inverse ratio of 3 : 2 is 1/3 : 1/2. Step 2: Multiply by the LCM of 3, 2 to clear fractions: 2 : 3. Step 3: Total parts = 5; 1 part = 1400 ÷ 5 = 280, so A = 2 × 280 = ₹560.

Question 3

Hard

Mixture A contains milk and water in the ratio 3 : 2, and mixture B in the ratio 9 : 7. In what ratio must A and B be mixed to get a mixture with milk and water in the ratio 23 : 17?

A 1 : 2

B 2 : 1

C 1 : 1

D 1 : 3

Correct Answer: A

Explanation:

Step 1: Express milk as a fraction of each mixture: A = 3/5 = 3/5, B = 9/16 = 9/16, required = 23/40 = 23/40. Step 2: By alligation, A : B = (B's fraction − required) : (required − A's fraction), taking positive differences: |9/16 − 23/40| : |23/40 − 3/5| = 1/80 : 1/40. Step 3: Simplify: 1 : 2.

Question 4

Easy

What is the triplicate ratio of 2 : 3?

A 8 : 27

B 2 : 3

C 27 : 8

D 1 : 3

Correct Answer: A

Explanation:

Step 1: The triplicate ratio of a : b is obtained when you cube each term. Step 2: 2³ : 3³ = 8 : 27. Step 3: 8 : 27 is already in its simplest form.

Question 5

Easy

A purse contains ₹1 coins and 50-paise coins in the ratio 9 : 5. If the total value is ₹414, how many 50-paise coins are there?

A 324 coins

B 504 coins

C 180 coins

D 216 coins

Correct Answer: C

Explanation:

Step 1: Let the numbers of coins be 9k (₹1) and 5k (50 paise). Step 2: Total value = 9k × ₹1 + 5k × ₹0.50 = ₹11.5k = ₹414, so k = 36. Step 3: 50-paise coins = 5 × 36 = 180.

Ratio and Proportion Practice Questions