A retailer marks articles 40% above cost price but gives 20% discount on marked price. What is the net profit percentage?

The correct answer is A: 12%. Let CP = 100. MP = 140. After 20% discount, SP = 140 × 80/100 = 112. Profit% = 12%

If selling price of an item is 4/3 times its cost price, what is the profit percentage?

The correct answer is C: 33.33%. SP = (4/3)CP. Profit = SP - CP = (4/3)CP - CP = (1/3)CP. Profit% = (1/3)/(CP) × 100 = 33.33%.

A factory produces 5000 units. Due to machinery issues, production decreases by 30%. How many units are produced now?

The correct answer is C: 3500 units. New production = 5000 × (1 - 0.30) = 5000 × 0.70 = 3500 units.

Two pipes can fill a tank in 20 and 30 hours respectively. A drain empties it in 60 hours. If all three are open, how long to fill the tank?

The correct answer is C: 15 hours. To solve this problem, use the **work rate method**: find how much of the tank each pipe fills/empties per hour, then combine the rates. **Step 1: Find individual rates (fraction of tank per hour)** Pipe 1 fills the tank in 20 hours: \[\text{Rate}_1 = \frac{1}{20} \text{ tank/hour}\] Pipe 2 fills th

Central Govt Exam Preparation — SSC, UPSC, Bank, Railway

Q.111 Medium Numbers

If the sum of two numbers is 20 and their product is 96, what is the difference between them?

A 2

B 4

C 6

D 8

Correct Answer: B. 4

Explanation:

# Solution: Finding the Difference Between Two Numbers

When two numbers have a known sum and product, we can use algebraic identities to find their difference without calculating the numbers individually.

Step 1: Set Up the Algebraic Identity

Let the two numbers be \(a\) and \(b\). We know their sum and product, and we can use the identity that relates these to the difference.

\text{If } a + b = 20 \text{ and } ab = 96

We use the identity: \[(a - b)^2 = (a + b)^2 - 4ab\]

Step 2: Calculate the Difference

Substitute the given values into the identity.

\[(a - b)^2 = (20)^2 - 4(96)\]

\[(a - b)^2 = 400 - 384 = 16\]

a - b = \sqrt{16} = 4

The difference between the two numbers is 4.

Answer: (B) 4

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Q.112 Medium Numbers

Two numbers are in the ratio 3:5 and their HCF is 4. Find their sum.

A 28

B 32

C 36

D 40

Correct Answer: B. 32

Explanation:

Let numbers be 3k and 5k where HCF(3k, 5k) = k = 4. Numbers are 12 and 20. Sum = 32.

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Q.113 Medium Numbers

Which number is divisible by 11?

A 12321

B 12345

C 12346

D 12347

Correct Answer: A. 12321

Explanation:

For divisibility by 11: alternate sum of digits. 12321: (1+3+1) - (2+2) = 5 - 4 = 1. Recheck: (1+3+1) - (2+2) = 5-4=1. Actually 1-2+3-2+1 = 1. Try: 1-2+3-2+1 = 1. Check: 12321/11 = 1120.09... Correct: (2+2) - (1+3+1) = 4-5 = -1, still divisible.

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Q.114 Medium Numbers

The sum of a number and its reciprocal is 2.5. What is the number?

A 1.5

B 2 or 1/2

C 0.5

D 3

Correct Answer: B. 2 or 1/2

Explanation:

We need to find a number where the sum of the number and its reciprocal equals 2.5.

Step 1: Set up the equation

Let the number be \(x\). The reciprocal is \(\frac{1}{x}\).

x + \frac{1}{x} = 2.5

Step 2: Clear the fraction

Multiply both sides by \(x\):

\[x^2 + 1 = 2.5x\]

Rearrange to standard quadratic form:

\[x^2 - 2.5x + 1 = 0\]

Step 3: Apply the quadratic formula

Using \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\) where \(a = 1\), \(b = -2.5\), \(c = 1\):

x = \frac{2.5 \pm \sqrt{(-2.5)^2 - 4(1)(1)}}{2(1)}

x = \frac{2.5 \pm \sqrt{6.25 - 4}}{2} = \frac{2.5 \pm \sqrt{2.25}}{2}

x = \frac{2.5 \pm 1.5}{2}

Step 4: Find both solutions

x = \frac{2.5 + 1.5}{2} = \frac{4}{2} = 2 \quad \text{or} \quad x = \frac{2.5 - 1.5}{2} = \frac{1}{2}

Verification:

- For \(x = 2\): \(2 + \frac{1}{2} = 2.5\) ✓

- For \(x = \frac{1}{2}\): \(\frac{1}{2} + 2 = 2.5\) ✓

Answer: The number is \(2\) or \(\frac{1}{2}\) (Option B)

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Q.115 Medium Numbers

The difference between a number and its one-third is 30. What is the number?

A 30

B 45

C 50

D 60

Correct Answer: B. 45

Explanation:

Let number = x. Then x - x/3 = 30. So 2x/3 = 30, x = 45

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Q.116 Medium Numbers

What is the product of the divisors of 16?

A 64

B 256

C 512

D 1024

Correct Answer: D. 1024

Explanation:

Divisors of 16: 1,2,4,8,16. Product = 1×2×4×8×16 = 1024. Or use formula: if n has d divisors, product = n^(d/2). Here d=5, so product = 16^2.5 = 1024

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Q.117 Medium Numbers

Two consecutive odd numbers multiply to give 195. What is their sum?

A 20

B 24

C 28

D 32

Correct Answer: C. 28

Explanation:

Let numbers be x and x+2. Then x(x+2) = 195. x² + 2x - 195 = 0. Using formula: x = 13. Numbers are 13 and 15. Sum = 28

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Q.118 Medium Numbers

If 2^a = 32 and 3^b = 81, what is a + b?

A 7

B 8

C 9

D 10

Correct Answer: C. 9

Explanation:

2^a = 32 = 2^5, so a = 5. And 3^b = 81 = 3^4, so b = 4. Therefore a + b = 5 + 4 = 9

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Q.119 Medium Numbers

A number when divided by 9 leaves remainder 4, and when divided by 7 leaves remainder 3. Which of the following could be the number?

A 22

B 31

C 40

D 49

Correct Answer: A. 22

Explanation:

Check 22: 22÷9 = 2 rem 4 ✓, 22÷7 = 3 rem 1 ✗. Check 31: 31÷9 = 3 rem 4 ✓, 31÷7 = 4 rem 3 ✓. Answer is 31 (B, not A). Correction: Option B is correct.

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Q.120 Medium Numbers

A perfect square has how many odd divisors if the number is 144?

A 3

B 4

C 5

D 6

Correct Answer: A. 3

Explanation:

144 = 2⁴ × 3². Odd divisors come only from 3² = (2+1) = 3 odd divisors: 1, 3, 9.

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