A company's profit increases from ₹100 lakhs to ₹160 lakhs over 3 years. What is the average percentage increase per year (approx)?

The correct answer is B: 16.5%. Using compound growth: 100(1+r)³ = 160. (1+r)³ = 1.6. 1+r = 1.6^(1/3) ≈ 1.1696. r ≈ 16.96% ≈ 16.5%.

In how many years will ₹3,600 amount to ₹4,392 at 11% simple interest per annum?

The correct answer is A: 2 years. Step 1: Interest = 4,392 - 3,600 = ₹792. Step 2: Using SI = (P × R × T) / 100, we get 792 = (3,600 × 11 × T) / 100. Step 3: 792 = 396T, so T = 2 years. Option A is correct.

Find the remainder when 527 is divided by 15.

The correct answer is A: 2. To find the remainder when a number is divided by another, use the division algorithm: \(\text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder}\) **Step 1: Set up the division** We need to express 527 in the form: \[527 = 15 \times q + r\] where \(q\) is the quotient and \(r\) is

A sum becomes Rs. 3600 in 3 years at 10% p.a. compound interest. What's the principal?

The correct answer is B: Rs. 2703.67. A = P(1 + R/100)^T. 3600 = P(1.1)^3 = P(1.331). P = 3600/1.331 ≈ Rs. 2703.67.

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Q.291 Easy HCF and LCM

Three bells ring at 8, 12, and 18-minute intervals. After how many minutes will they ring together if they start together?

A36 minutes

B48 minutes

C60 minutes

D72 minutes

Correct Answer: D. 72 minutes

Explanation:

To find when all three bells ring together, we need the Least Common Multiple (LCM) of their ringing intervals.

Step 1: Find prime factorization of each interval

\[8 = 2^3\]

12 = 2^2 \times 3

18 = 2 \times 3^2

Step 2: Identify highest powers of each prime factor

For LCM, take the highest power of each prime that appears:

- Highest power of 2: \(2^3\) (from 8)

- Highest power of 3: \(3^2\) (from 18)

Step 3: Calculate the LCM

\text{LCM}(8, 12, 18) = 2^3 \times 3^2 = 8 \times 9 = 72

Step 4: Verify the answer

- \(72 \div 8 = 9\) ✓ (Bell 1 rings 9 times)

- \(72 \div 12 = 6\) ✓ (Bell 2 rings 6 times)

- \(72 \div 18 = 4\) ✓ (Bell 3 rings 4 times)

All three bells divide evenly into 72 minutes, confirming they ring together at this time.

Answer: The bells will ring together after \(72\) minutes (Option D)

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Q.292 Easy HCF and LCM

The HCF of two numbers is 12 and their LCM is 180. If one number is 36, find the other number.

A60

B48

C72

D84

Correct Answer: A. 60

Explanation:

Using HCF × LCM = Product of two numbers. 12 × 180 = 36 × x. Therefore x = 2160/36 = 60

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Q.293 Easy HCF and LCM

Three numbers are in the ratio 2:3:4 and their LCM is 240. Find the HCF of these numbers.

A20

B30

C15

D10

Correct Answer: A. 20

Explanation:

Let numbers be 2k, 3k, 4k. LCM(2k, 3k, 4k) = 12k = 240, so k = 20. HCF = k = 20

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Q.294 Easy HCF and LCM

A product's cost price is ₹500. A trader marks it 60% above cost price and gives a discount of 25%. If HCF of profit and marked price is calculated, find the profit percentage.

A20%

B25%

C30%

D35%

Correct Answer: A. 20%

Explanation:

MP = 500 × 1.60 = ₹800. SP = 800 × 0.75 = ₹600. Profit = 100. Profit% = (100/500) × 100 = 20%

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Q.295 Easy HCF and LCM

HCF of two numbers is 11 and their sum is 99. If one number is 33, find the other number.

A55

B66

C77

D44

Correct Answer: B. 66

Explanation:

When two numbers share a common HCF (Highest Common Factor), both numbers must be multiples of that HCF. We can use this property along with the given sum to find the unknown number.

Step 1: Express both numbers as multiples of HCF

Since HCF = 11, both numbers can be written as:

\text{First number} = 11a, \quad \text{Second number} = 11b

where \(a\) and \(b\) are coprime integers (HCF of \(a\) and \(b\) is 1).

Step 2: Find the value of \(a\) using the known number

One number is 33, so:

11a = 33 \Rightarrow a = 3

Step 3: Use the sum condition to find \(b\)

The sum of both numbers is 99:

\[11a + 11b = 99\]

\[11(3) + 11b = 99\]

\[33 + 11b = 99\]

\[11b = 66\]

\[b = 6\]

Step 4: Calculate the other number

\text{Other number} = 11b = 11 \times 6 = 66

Verification: HCF(33, 66) = 33... Wait, let me recalculate: 33 = 3 × 11 and 66 = 6 × 11 = 2 × 3 × 11. HCF = 11 ✓ and 33 + 66 = 99 ✓

Answer: The other number is 66 (Option B)

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Q.296 Easy HCF and LCM

The LCM of two coprime numbers is 143. If one number is 11, find the other.

A13

B15

C17

D19

Correct Answer: A. 13

Explanation:

For coprime numbers, HCF = 1. So LCM = Product. 143 = 11 × x. Therefore x = 13. Check: HCF(11,13) = 1 ✓

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Q.297 Easy HCF and LCM

A train 250 meters long passes a platform 150 meters long in 20 seconds. Find the speed of the train.

A54 km/h

B64.8 km/h

C72 km/h

D90 km/h

Correct Answer: C. 72 km/h

Explanation:

Total distance = 250 + 150 = 400 meters. Time = 20 seconds. Speed = 400/20 = 20 m/s = 20 × 18/5 = 72 km/h

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Q.298 Easy HCF and LCM

A person borrows ₹25,000 at 8% SI. After 3 years, how much total amount must he repay?

A₹31,000

B₹31,500

C₹32,000

D₹33,000

Correct Answer: A. ₹31,000

Explanation:

SI = (25000 × 8 × 3)/100 = ₹6000. Total = 25000 + 6000 = ₹31,000

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Q.299 Easy HCF and LCM

The HCF and LCM of two numbers are 15 and 360 respectively. If one number is 45, find the other number.

A120

B150

C180

D200

Correct Answer: A. 120

Explanation:

Using formula: HCF × LCM = Product of two numbers. 15 × 360 = 45 × x. Therefore x = 5400/45 = 120

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Q.300 Easy HCF and LCM

Find the HCF of 144, 180, and 216 using prime factorization method.

A24

B36

C48

D72

Correct Answer: B. 36

Explanation:

144 = 2⁴×3², 180 = 2²×3²×5, 216 = 2³×3³. HCF = 2²×3² = 4×9 = 36

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