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1.
If A : B = 5 : 6 and B : C = 4 : 9, then A : B : C = ?
Correct Answer: E [10 : 12 : 27]
Explanation:
Bridge Link: 5 × 4 : 6 × 4 : 6 × 9 = 20 : 24 : 54 = 10 : 12 : 27.
2.
₹ 3,600 is divided among A, B and C in the ratio 1/3 : 1/4 : 1/6. C's share is:
Correct Answer: C [₹ 800]
Explanation:
× 12 → 4 : 3 : 2 (9 parts) → 1 part = 400 → C = ₹ 800.
3.
What number must be added to each term of 7 : 11 to make the ratio 3 : 4?
Correct Answer: D [5]
Explanation:
(7 + x)/(11 + x) = 3/4 → 28 + 4x = 33 + 3x → x = 5.
4.
The incomes of A and B are in the ratio 4 : 3 and their expenditures in 3 : 2. If each saves ₹ 6,000, A's income is:
Correct Answer: B [₹ 24,000]
Explanation:
4x − 3y = 6,000 and 3x − 2y = 6,000 → x = 6,000 → A = ₹ 24,000.
5.
A starts a business with ₹ 25,000. After 3 months B joins with ₹ 30,000. Out of a year-end profit of ₹ 38,000, B gets:
Correct Answer: A [₹ 18,000]
Explanation:
25 × 12 : 30 × 9 = 300 : 270 = 10 : 9 → B = 9/19 × 38,000 = ₹ 18,000.
6.
The average weight of 35 students is 48 kg. When the teacher's weight is included, the average rises by 1 kg. The teacher weighs:
Correct Answer: C [84 kg]
Explanation:
Average Shift: 48 + 36 × 1 = 84 kg.
7.
The average of 10 numbers increases by 1.5 when one number, 45, is replaced by a new number. The new number is:
Correct Answer: E [60]
Explanation:
45 + 10 × 1.5 = 60.
8.
25 boys average 70 marks and 15 girls average 78 marks. The class average is:
Correct Answer: A [73]
Explanation:
(1,750 + 1,170)/40 = 2,920/40 = 73.
9.
The ages of P and Q are in the ratio 7 : 5. After 8 years the ratio will be 9 : 7. The sum of their present ages is:
Correct Answer: B [48]
Explanation:
Gaps 2 and 2 → 7 → 9 is 2 parts = 8 years → 1 part = 4 → 28 + 20 = 48.
10.
The sum of the present ages of A and B is 50 years. Five years ago their ages were in the ratio 3 : 2. A's present age is:
Correct Answer: D [29]
Explanation:
Five years ago the sum was 40 → 24 and 16 → A = 24 + 5 = 29.
11.
Quantity I: the third proportional to 16 and 24
Quantity II: the mean proportional between 18 and 72
Quantity II: the mean proportional between 18 and 72
Correct Answer: E [Quantity I = Quantity II or relation cannot be established]
Explanation:
I: 24²/16 = 36. II: √(18 × 72) = √1,296 = 36.
12.
What is Ravi's present age?
I. Ravi is 4 years older than Sita.
II. The ratio of Ravi's age to Sita's age is 5 : 4.
I. Ravi is 4 years older than Sita.
II. The ratio of Ravi's age to Sita's age is 5 : 4.
Correct Answer: D [Both statements together are needed]
Explanation:
I gives only the gap; II only the ratio.
13.
Trick Spotter: 35% of A equals 21% of B. The fastest way to find A : B is:
Correct Answer: B [Swap the percentages: A : B = 21 : 35 = 3 : 5]
Explanation:
Fraction Swap: p% of A = q% of B → A : B = q : p = 21 : 35 = 3 : 5.
14.
Which of the following is/are correct?
I. The compound ratio of 2 : 3 and 9 : 4 is 3 : 2.
II. The sub-duplicate ratio of 36 : 81 is 2 : 3.
III. The triplicate ratio of 2 : 5 is 6 : 15.
I. The compound ratio of 2 : 3 and 9 : 4 is 3 : 2.
II. The sub-duplicate ratio of 36 : 81 is 2 : 3.
III. The triplicate ratio of 2 : 5 is 6 : 15.
Correct Answer: C [Only I and II]
Explanation:
I: 18 : 12 = 3 : 2 ✓. II: 6 : 9 = 2 : 3 ✓.
15.
Reverse question: a sum is divided between X and Y in the ratio 5 : 3 and Y gets ₹ 2,400. The sum is:
Correct Answer: B [₹ 6,400]
Explanation:
3 parts = 2,400 → 1 part = 800 → 8 parts = ₹ 6,400.
16.
Spot My Mistake: "A invests ₹ 20,000 for the whole year and B invests ₹ 30,000 after 4 months. Ratio = 20 × 12 : 30 × 4 = 2 : 1." Which statement is correct?
Correct Answer: B [B's money worked for 8 months, so the ratio is 240 : 240 = 1 : 1]
Explanation:
Joining after 4 months → 12 − 4 = 8 months: 20 × 12 = 240 = 30 × 8.
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