Quantitative Aptitude - MCQ Practice Questions

Let numbers be 3x and 5x. 3x + 5x = 160. 8x = 160. x = 20. Larger number = 5×20 = 100

Percentage = 0.35 × 0.60 × 100 = 21%

To find the profit percentage, we need to track the marked price and selling price relative to cost price.

Step 1: Assume a Cost Price

Let the cost price be $\text{CP}=100$ (using a convenient base value)

Step 2: Calculate Marked Price

The merchant marks goods 40% above cost price:

Step 3: Calculate Selling Price

A 25% discount is given on the marked price:

Step 4: Calculate Profit Percentage

Profit is the difference between selling price and cost price:

Profit percentage:

**Answer: The profit percentage is $5\%$ (Option A)**

Distance = 240 + 360 = 600m. Speed = $\frac{600}{30}$ = 20 m/s = 20 × 3.6 = 72 km/h.

SI = (P × R × T)/100 = (5000 × 8 × 4)/100 = 1600.

We need to find the original number first, then calculate 65% of it using the given condition that 45% of the number equals 180.

Step 1: Set up the equation

Let the unknown number be $x$. We're told that 45% of this number is 180.

Step 2: Solve for the number

Divide both sides by 0.45 to isolate $x$:

Step 3: Calculate 65% of the number

Now that we know the number is 400, we find 65% of it:

**Answer: 65% of the number is $260$ (Option A)**

Let numbers be 4x and 7x. 7x - 4x = 45, 3x = 45, x = 15. Larger = 7 × 15 = 105.

SP = 450 × 1.40 = 630.

When a number undergoes successive percentage changes, we apply each change sequentially to find the net effect. Let's use a base value to track the changes.

Step 1: Apply the 25% increase

Let the original number be $x$.

After a 25% increase:

Step 2: Apply the 20% decrease

Now decrease this result by 20%:

Step 3: Calculate the final multiplier

So the final value equals $1\times x=x$ (the original number).

Step 4: Determine net percentage change

Since the final value equals the original value:

Answer: The net change is 0% (Option A)

Key insight: A 25% increase multiplies by 1.25, and a 20% decrease multiplies by 0.80. Since $1.25\times 0.80=1.00$, the changes perfectly cancel out.

To find the selling price, we use the profit formula: Selling Price = Cost Price + Profit, where profit is calculated as a percentage of the cost price.

Step 1: Identify given information

Cost Price (C.P.) = Rs. 80

Profit % = 37.5%

Step 2: Convert profit percentage to a fraction

Step 3: Calculate profit amount

Step 4: Calculate selling price

Answer: The selling price is Rs. 110 (Option A)

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Quick Check: Using the formula $\text{S.P.}=\text{C.P.}\left(1+\frac{\text{Profit}\%}{100}\right)=80\left(1+0.375\right)=80\times 1.375=110$ ✓

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

Net rate = $\frac{1}{6}$ - $\frac{1}{10}$ = $\frac{5}{30}$ - $\frac{3}{30}$ = $\frac{2}{30}$ = $\frac{1}{15}$. Time = 15 hours.

SI = (P × R × T) / 100 = (5000 × 8 × 2.5) / 100 = $\frac{100000}{100}$ = Rs. 1000.

Downstream speed = $\frac{48}{4}$ = 12 km/h. Upstream speed = $\frac{48}{6}$ = 8 km/h. Current speed = (12 - 8)/2 = 2 km/h.

Amount = P(1 + R/100)^T = 10000(1.1)^2 = 10000 × 1.21 = Rs. 12100.

Let original number = x. x × 1.15 = 575. x = $\frac{575}{1}$.15 = 500.

CP = 50 × 3 = 150. SP = 50 × 3.5 = 175. Profit % = ($\frac{25}{150}$) × 100 = 16.67%.

Downstream = 15 + 3 = 18. Upstream = 15 - 3 = 12. Ratio = 18:12 = 3:2.

Work = Workers × Days = 75 × 120 = 9000. Days = $\frac{9000}{90}$ = 100 days.

Selling Price = 500 × $\frac{80}{100}$ = Rs. 400. If profit is 25%, then CP = 400 × $\frac{100}{125}$ = Rs. 320