CMAT questions on Arithmetic - Ratio, Proportion & Variation

Asked: the coins Purab originally received.

Coins that left the three sons = 30 + 30 + 25 = 85.

Coins remaining = 2505 − 85 = 2420.

The remaining coins are in the ratio 46 : 41 : 34 (sum 121), so 1 part = 2420 / 121 = 20.

Purab now has 41 × 20 = 820. He received 820 + 30 = 850.

Check: Brij 920 + 30 = 950 and Mohan 680 + 25 = 705. 950 + 850 + 705 = 2505. ✓

Answer: 850

Matching ratio terms:

• A: the duplicate ratio of a : b is a² : b². For 2 : 7 that is 4 : 49, which is (II).
• B: the compound ratio multiplies the antecedents and the consequents. (2 × 5 × 4) : (7 × 3 × 7) = 40 : 147, which is (III).
• C: 2 : 7 = 4 : 14 (both terms × 2), which is (IV).
• D: 5 : 6 = 25 : 30 (both terms × 5), which is (I).

Matching: A–II, B–III, C–IV, D–I.

Answer: option 2

Check each statement:

• A: 1/x : 1/y : 1/z = 2 : 3 : 5, so x : y : z = 1/2 : 1/3 : 1/5. Multiply by 30 to get 15 : 10 : 6. True.
• B: let 4p = 6q = 9r = 36. Then p = 9, q = 6, r = 4, so p : q : r = 9 : 6 : 4. True.
• C: let 2A = 3B = 4C = 12. Then A = 6, B = 4, C = 3, so the ratio is 6 : 4 : 3, not 3 : 4 : 6. False.
• D: P/Q = 2/3, Q/R = 3/4, R/P = 4/2 = 2. Multiply by 12 to get 8 : 9 : 24, not 9 : 8 : 24. False.

Answer: (A) and (B) only (option 3)

Key idea: rent is shared in the ratio of sheep × months (sheep-months).

• Anil: 24 × 3 = 72
• Bimal: 10 × 5 = 50
• Champak: 35 × 4 = 140
• Damodar: 21 × 3 = 63

Total = 72 + 50 + 140 + 63 = 325 sheep-months.

Anil's 72 units cost Rs 720, so 1 unit = Rs 10.

Total rent = 325 × 10 = Rs 3,250.

Answer: Rs. 3,250