Quantitative Aptitude - MCQ Practice Questions

Amount = P(1+R/100)² = 10000(1.1)² = 10000×1.21 = ₹12,100. CI = 12100 - 10000 = ₹2100

HCF × LCM = a × b. 6 × 180 = 30 × b. 1080 = 30b. b = 36

264 = 2³×3×11, 396 = 2²×3²×11, 528 = 2⁴×3×11. HCF = 2²×3×11 = 4×3×11 = 132

# Solution: Finding Pairs with Given HCF and LCM

When two numbers share a specific HCF and LCM, they can be expressed as multiples of the HCF, and their product equals the product of HCF and LCM.

Step 1: Express Numbers in Terms of HCF

Since HCF = 18, both numbers must be multiples of 18. Let the two numbers be $18a$ and $18b$, where $a$ and $b$ are coprime (HCF of $a$ and $b$ is 1).

Step 2: Use the HCF-LCM Product Formula

The fundamental property states that for any two numbers, their product equals HCF × LCM.

Step 3: Find Coprime Factor Pairs of 24

We need pairs $(a,b)$ such that $ab=24$ and HCF$(a,b)=1$ (coprime pairs).

Factorizations of 24: $1\times 24$, $2\times 12$, $3\times 8$, $4\times 6$

Checking which are coprime:

Step 4: Find the Number Pairs

The coprime pairs are $(1,24)$ and $(3,8)$, giving us:

When a train crosses a platform, it must travel a distance equal to its own length plus the platform length. We'll use the relationship between speed, distance, and time.

Step 1: Convert speed to m/s

The train travels at $60\text{km/h}$. Convert to metres per second:

Step 2: Calculate total distance traveled

The train crosses the platform in 30 seconds. Using $\text{Distance}=\text{Speed}\times \text{Time}$:

Step 3: Apply the crossing condition

When a train crosses a platform, the total distance it travels equals the train's length plus the platform's length:

Step 4: Solve for train length

**Answer: The length of the train is $200\text{m}$ (Option A)**

96 = 2^5 × 3, 144 = 2^4 × 3^2, 192 = 2^6 × 3. HCF = 2^4 × 3 = 16 × 3 = 48

Amount = P(1 + r/100)^t = 8000(1.1)^2 = 8000 × 1.21 = ₹9680. CI = 9680 - 8000 = ₹1680

When selling multiple articles at different profit/loss percentages with equal cost prices, we calculate the overall result by comparing total selling price to total cost price.

Step 1: Calculate selling price of first article (20% profit)

Cost price of first article = ₹1000

Selling price with 20% profit:

Step 2: Calculate selling price of second article (20% loss)

Cost price of second article = ₹1000

Selling price with 20% loss:

Step 3: Find total cost price and total selling price

Step 4: Calculate overall profit or loss

Since the total selling price equals the total cost price, there is no profit and no loss.

Answer: No profit, no loss (Option A)

Let numbers be 4k and 5k. HCF = k = 8. So numbers are 32 and 40

Filling rate = $\frac{1}{10}$, Emptying rate = $\frac{1}{15}$. Net rate = $\frac{1}{10}$ - $\frac{1}{15}$ = $\frac{3}{30}$ - $\frac{2}{30}$ = $\frac{1}{30}$. Time = 30 hours

After 30% discount: 1500 × 0.7 = ₹1050. After additional 10%: 1050 × 0.9 = ₹945

Let manufacturer's CP = x. Wholesaler's CP = 1.2x. Retailer's CP = 1.2x × 1.25 = 1.5x. Customer pays = 1.5x × 1.3 = 1.95x = 1,950. So x = 1,000.

Article 1: CP₁ = $\frac{1200}{1}$.2 = ₹1,000. Article 2: CP₂ = $\frac{1200}{0}$.8 = ₹1,500. Total CP = ₹2,500, Total SP = ₹2,400. Loss = 4%.

SP = MP × 0.8 × 0.85 = MP × 0.68 = 1,292. MP = 1,$\frac{292}{0}$.68 = ₹1,900.

CP of 200 eggs = ($\frac{200}{12}$) × 12 = ₹200. SP = (120 × 1.5) + (80 × 1) = 180 + 80 = ₹260. Profit = $\frac{60}{200}$ × 100 = 25%.

To find the selling price for a desired profit, we must first find the cost price using the loss information, then calculate the new selling price for the desired gain.

Step 1: Find the Cost Price (CP)

When selling at ₹5 per kg results in a 10% loss, we use:

Step 2: Calculate Selling Price for 15% Gain

For a 15% gain, the selling price should be:

Step 3: Simplify

Answer: ₹6.39 per kg (Option A)

SP = 2,000 × 0.8 × 0.9 × 0.95 = 2,000 × 0.684 = ₹1,368.

To find profit, we must track the cost price (including transportation) and selling price (after markup and discount).

Step 1: Calculate total cost price

The merchant buys goods for ₹6,000 and pays 10% extra for transportation:

Step 2: Calculate marked price

He marks up the goods by 25% on the cost price:

Step 3: Calculate selling price after discount

He offers a discount of 8% on the marked price:

Step 4: Calculate profit

Answer: The profit is ₹990 (Option A)

Let CP = 3x, MP = 5x. SP = 5x × 0.8 = 4x. Profit = 4x - 3x = x. Profit% = x/3x × 100 = 33.33%.

Let CP = 100. Current SP = 75 (25% loss). Desired SP = 125 (25% profit). Increase = 125 - 75 = 50. Percentage increase = $\frac{50}{75}$ × 100 = 66.67%.