Quantitative Aptitude - MCQ Practice Questions

HCF×LCM = product of numbers. 16×960 = 15,360.

Using HCF × LCM = Product of two numbers: 18 × 1080 = 108 × x; x = $\frac{19440}{108}$ = 180

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

Step 1: Find the prime factorization of each interval

Step 2: Determine the LCM

The LCM is found by taking the highest power of each prime factor:

Step 3: Add 90 minutes to the initial time

The bells ring together at 9:00 AM. They will ring together again after 90 minutes.

Step 4: Calculate the final time

Answer: The three bells will ring together again at 10:30 AM (Option D)

To find the effective profit percentage, we need to track the cost price, marked selling price (with profit), and discounted selling price.

Step 1: Calculate the Marked Selling Price (with 25% profit)

The shopkeeper marks up books at a 25% profit on the cost price of ₹20.

Step 2: Calculate the Actual Selling Price (after 10% discount)

During the sale, a 10% discount is given on the marked price of ₹25.

Step 3: Calculate the Effective Profit

Step 4: Calculate Effective Profit Percentage

Answer: The effective profit percentage is 12.5% (Option A)

To find the LCM of 48, 64, and 96, we express each number as a product of prime factors, then take the highest power of each prime that appears.

Step 1: Prime factorization of each number

Divide each number by its prime factors:

Step 2: Identify all prime factors

The prime factors present are: $2$ and $3$

Step 3: Take the highest power of each prime

Step 4: Calculate the LCM

**Answer: The LCM of 48, 64, and 96 is $192$ (Option A)**

Combined rate = $\frac{1}{12}$ + $\frac{1}{18}$ = $\frac{3}{36}$ + $\frac{2}{36}$ = $\frac{5}{36}$; Time = $\frac{36}{5}$ = 7.2 days

After 15% discount: 85%; After 10% on that: 85×$\frac{90}{100}$ = 76.5%; Single discount = 100-76.5 = 23.5%

Profit = 20% of CP; ₹200 = 0.2×CP; CP = ₹1000; SP = 1000 + 200 = ₹1200

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

Step 2: Identify highest powers of each prime factor

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

Step 3: Calculate the LCM

Step 4: Verify the answer

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)**

Using HCF × LCM = Product of two numbers. 12 × 180 = 36 × x. Therefore x = $\frac{2160}{36}$ = 60

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

MP = 500 × 1.60 = ₹800. SP = 800 × 0.75 = ₹600. Profit = 100. Profit% = ($\frac{100}{500}$) × 100 = 20%

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

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

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

Using formula: HCF × LCM = Product of two numbers. 15 × 360 = 45 × x. Therefore x = $\frac{5400}{45}$ = 120

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

Speed = $\frac{360}{6}$ = 60 km/h. Time = Distance/Speed = $\frac{600}{60}$ = 10 hours

24 = 2³×3, 36 = 2²×3². LCM = 2³×3² = 8×9 = 72

SI = (P×R×T)/100 = (8000×6×2.5)/100 = $\frac{120000}{100}$ = ₹1200