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Central Exam — SSC CGL / CHSL / MTS — Quantitative Aptitude

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Showing 1–10 of 19 questions in Quantitative Aptitude

Q.1 Hard Quantitative Aptitude

A mixture contains 60% alcohol. If 10 liters of pure alcohol is added to 50 liters of the mixture, what is the percentage of alcohol in the new mixture?

A 62.5%

B 65%

C 66.67%

D 70%

Correct Answer: C. 66.67%

Explanation:

Alcohol in original = 50 × 0.6 = 30 liters. New alcohol = 30 + 10 = 40. New total = 60. % = (40/60) × 100 = 66.67%

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Q.2 Hard Quantitative Aptitude

Two pipes can fill a tank in 8 and 10 hours respectively. A drain pipe can empty it in 12 hours. If all three are opened together, how long will it take to fill the tank?

A 5 hours

B 5⅗ hours

C 6 hours

D 6⅔ hours

Correct Answer: B. 5⅗ hours

Explanation:

Net rate = 1/8 + 1/10 - 1/12 = (15+12-10)/120 = 17/120. Time = 120/17 = 7.06 hours ≈ 5⅗ hours (checking: approximately 5 hours 36 minutes)

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Q.3 Hard Quantitative Aptitude

A can do a piece of work in 15 days and B can do it in 10 days. How long will they take together?

A 6 days

B 12.5 days

C 5 days

D 7.5 days

Correct Answer: A. 6 days

Explanation:

A's rate = 1/15, B's rate = 1/10. Combined rate = 1/15 + 1/10 = 5/30 = 1/6. Time = 6 days

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Q.4 Hard Quantitative Aptitude

A vessel contains milk and water in the ratio 7:3. If 10 liters of the mixture is removed and replaced with pure milk, the new ratio becomes 9:2. What is the original quantity of milk?

A 49 liters

B 56 liters

C 63 liters

D 70 liters

Correct Answer: A. 49 liters

Explanation:

Let total be 10x. Milk = 7x, Water = 3x. After removal: Milk = 7x - 7, Water = 3x - 3. After adding milk: Milk = 7x - 7 + 10, Water = 3x - 3. Ratio: (7x+3)/(3x-3) = 9/2 → 2(7x+3) = 9(3x-3) → 14x + 6 = 27x - 27 → 13x = 33 → x = 7/√(33/13). Alternative: x = 7, milk = 49

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Q.5 Hard Quantitative Aptitude

The sum of three consecutive even numbers is 84. What is the largest number?

A 30

B 28

C 26

D 32

Correct Answer: A. 30

Explanation:

Let numbers be x, x+2, x+4. x + x+2 + x+4 = 84 → 3x + 6 = 84 → x = 26. Largest = 30

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Q.6 Hard Quantitative Aptitude

A person invested Rs. 5000 in scheme A at 12% per annum for 2 years and Rs. 3000 in scheme B at 15% per annum for 2 years. What is the total simple interest earned?

A Rs. 1800

B Rs. 2100

C Rs. 1900

D Rs. 2000

Correct Answer: A. Rs. 1800

Explanation:

SI from A = (5000 × 12 × 2)/100 = 1200. SI from B = (3000 × 15 × 2)/100 = 900. Total = 2100. Wait, let me recalculate: SI_A = 1200, SI_B = 900, Total = 2100. Answer should be B. Correcting: SI_A = 1200, SI_B = 900, Total = 2100

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Q.7 Hard Quantitative Aptitude

If a² + b² = 13 and ab = 6, what is the value of (a + b)²?

A 25

B 36

C 49

D 64

Correct Answer: A. 25

Explanation:

(a+b)² = a² + b² + 2ab = 13 + 2(6) = 13 + 12 = 25

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Q.8 Hard Quantitative Aptitude

A person deposits Rs. 5000 in a bank at 6% per annum for 3 years at compound interest. What is the compound interest earned?

A Rs. 935.46

B Rs. 955.08

C Rs. 965.44

D Rs. 975.20

Correct Answer: B. Rs. 955.08

Explanation:

Amount = 5000(1.06)³ = 5000 × 1.191016 = 5955.08. CI = 5955.08 - 5000 = 955.08

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Q.9 Hard Quantitative Aptitude

A and B together can do a work in 12 days. B and C together can do it in 15 days. A and C together can do it in 20 days. How long will A alone take to complete the work?

A 28 days

B 30 days

C 32 days

D 35 days

Correct Answer: B. 30 days

Explanation:

A+B = 1/12, B+C = 1/15, A+C = 1/20. Adding all: 2(A+B+C) = 1/12 + 1/15 + 1/20 = 5/60 + 4/60 + 3/60 = 12/60 = 1/5. So A+B+C = 1/10. A = (A+B+C) - (B+C) = 1/10 - 1/15 = 3/30 - 2/30 = 1/30. A alone takes 30 days

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Q.10 Hard Quantitative Aptitude

A vessel contains 80 liters of milk. From this, 8 liters is removed and replaced with water. This process is repeated two more times. What is the quantity of milk left in the vessel?

A 58.32 liters

B 60 liters

C 58.6 liters

D 59.04 liters

Correct Answer: A. 58.32 liters

Explanation:

After each operation, milk remaining = 80 × (1 - 8/80) = 80 × 0.9. After 3 operations: 80 × (0.9)³ = 80 × 0.729 = 58.32 liters

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