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1.  

In each question, compare Quantity I and Quantity II and choose: A) Quantity I > Quantity II, B) Quantity I < Quantity II, C) Quantity I ≥ Quantity II, D) Quantity I ≤ Quantity II, E) Quantity I = Quantity II or the relation cannot be established.

Quantity I: x, where x² − 21x + 110 = 0. Quantity II: 11.

Correct Answer: D [Quantity I ≤ Quantity II]

Explanation:

x = 10 or 11. 10 < 11 and 11 = 11 → Quantity I ≤ Quantity II.

2.  
The present ages of P and Q are in the ratio 3 : 4 and the product of their ages is 192. Quantity I: the age of one of them (P or Q). Quantity II: 12 years.

Correct Answer: C [Quantity I ≥ Quantity II]

Explanation:

12k² = 192 → k = 4 → ages 12 and 16.

3.  
The length of a rectangle is 4 m more than its breadth and its area is 96 m². Quantity I: the perimeter of the rectangle (m). Quantity II: the perimeter (m) of a square of side 11 m.

Correct Answer: B [Quantity I < Quantity II]

Explanation:

b² + 4b − 96 = 0 → b = 8 (−12 rejected), l = 12 → perimeter 40 m.

4.  
A car goes 120 km from P to Q at 40 km/h and returns at 60 km/h. Quantity I: its average speed for the whole journey (km/h). Quantity II: 45 km/h.

Correct Answer: A [Quantity I > Quantity II]

Explanation:

Time 3 h + 2 h = 5 h for 240 km → 48 km/h > 45 km/h.

5.  
Two fair dice are thrown. Quantity I: the probability that the sum is 8. Quantity II: 1/6.

Correct Answer: B [Quantity I < Quantity II]

Explanation:

Sum 8: (2,6), (3,5), (4,4), (5,3), (6,2) → 5/36 < 6/36 = 1/6.

6.  
Quantity I: 35% of 640. Quantity II: 40% of 560.

Correct Answer: E [Quantity I = Quantity II or relation cannot be established]

Explanation:

0.35 × 640 = 224; 0.40 × 560 = 224 → equal single values → E.

7.  
The sum of a number and its square is 72. Quantity I: the number. Quantity II: 8.

Correct Answer: D [Quantity I ≤ Quantity II]

Explanation:

n² + n − 72 = 0 → n = 8 or −9 (both allowed – the number is not said to be positive).

8.  
A can finish a work in 12 days and B in 18 days. Quantity I: the days A and B together take to finish it. Quantity II: 7 days.

Correct Answer: A [Quantity I > Quantity II]

Explanation:

1/12 + 1/18 = 5/36 → 36/5 = 7.2 days > 7 days.

9.  
Quantity I: the compound interest on ₹ 8,000 at 10% per annum for 2 years (compounded annually). Quantity II: the simple interest on ₹ 8,000 at 11% per annum for 2 years.

Correct Answer: B [Quantity I < Quantity II]

Explanation:

CI = 8,000 × 0.21 = ₹ 1,680; SI = 8,000 × 0.22 = ₹ 1,760 → I < II.

10.  
Quantity I: x, where x² − 9x + 20 = 0. Quantity II: y, where y² − 7y + 12 = 0.

Correct Answer: C [Quantity I ≥ Quantity II]

Explanation:

x = 4, 5; y = 3, 4. Pairs: 4 > 3, 4 = 4, 5 > 3, 5 > 4 → Quantity I ≥ Quantity II.

11.  
Quantity I: the number of ways in which the letters of the word WORD can be arranged. Quantity II: ⁴C₂ × 4.

Correct Answer: E [Quantity I = Quantity II or relation cannot be established]

Explanation:

4! = 24; ⁴C₂ × 4 = 6 × 4 = 24 → equal single values → E.

12.  
A boat's speed in still water is 12 km/h and the stream flows at 3 km/h. Quantity I: the time (hours) to go 36 km upstream. Quantity II: the time (hours) to go 45 km downstream.

Correct Answer: A [Quantity I > Quantity II]

Explanation:

Upstream 9 km/h → 36/9 = 4 h; downstream 15 km/h → 45/15 = 3 h → I > II.

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