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1.  
Three numbers are in the ratio 2 : 3 : 5 and the sum of their squares is 1,368. The largest number is:

Correct Answer: C [30]

Explanation:

4x² + 9x² + 25x² = 38x² = 1,368 → x = 6 → 30.

2.  
Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, the ratio becomes 12 : 23. The larger number is:

Correct Answer: D [55]

Explanation:

(3x − 9)/(5x − 9) = 12/23 → 69x − 207 = 60x − 108 → x = 11 → 55.

3.  
A, B and C invest in the ratio 3 : 4 : 5 for 8, 6 and 4 months respectively. Out of a profit of ₹ 51,000, C gets:

Correct Answer: A [₹ 15,000]

Explanation:

24 : 24 : 20 = 6 : 6 : 5 → C = 5/17 × 51,000 = ₹ 15,000.

4.  
The average of 11 results is 50. The average of the first six is 49 and of the last six is 52. The sixth result is:

Correct Answer: E [56]

Explanation:

294 + 312 − 550 = 56 (the sixth is counted twice).

5.  
Three years ago the average age of a family of 5 was 25 years. A baby has since been born, and the present average age of the 6 members is 23.5 years. The baby's age is:

Correct Answer: A [1 year]

Explanation:

Now the 5 total 125 + 15 = 140; 6 × 23.5 = 141 → baby = 1 year.

6.  
Eight years ago a father was 3 times as old as his son. Eight years hence he will be twice as old as his son. The father's present age is:

Correct Answer: D [56]

Explanation:

f − 8 = 3(s − 8) and f + 8 = 2(s + 8) → s = 24, f = 56.

7.  
A bag has ₹ 2, ₹ 1 and 50-paise coins in the ratio 3 : 4 : 6 (by number). The total value is ₹ 260. The number of 50-paise coins is:

Correct Answer: E [120]

Explanation:

Value ratio 6 : 4 : 3 → 13 parts = 260 → x = 20 → 50-paise coins = 6 × 20 = 120.

8.  
A invests ₹ 40,000 for 12 months and B invests ₹ 60,000 for 6 months. Profit ₹ 35,000.
Quantity I: A's share of the profit
Quantity II: ₹ 21,000

Correct Answer: B [Quantity I < Quantity II]

Explanation:

480 : 360 = 4 : 3 → A = 4/7 × 35,000 = ₹ 20,000 < ₹ 21,000.

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