Quantitative Aptitude - MCQ Practice Questions

Amount = 1000(1 + $\frac{10}{100}$)² = 1000 × 1.1 × 1.1 = Rs. 1210

Upstream speed = $\frac{30}{6}$ = 5 km/h. Downstream speed = $\frac{30}{3}$ = 10 km/h. Boat speed = (5+10)/2 = 7.5 km/h

Let original price = 100. After 25% increase = 125. After 20% decrease = 125 × $\frac{80}{100}$ = 100. Net = +5% gain

Combined rate = $\frac{1}{6}$ + $\frac{1}{8}$ + $\frac{1}{12}$ = $\frac{4}{24}$ + $\frac{3}{24}$ + $\frac{2}{24}$ = $\frac{9}{24}$

When two trains move towards each other, their relative speed is the sum of their individual speeds, and the total distance to cross is the sum of their lengths.

Step 1: Calculate total distance to be covered

When the trains cross each other completely, the total distance covered equals the sum of their lengths:

Step 2: Convert relative speed from m/s to km/h context

The trains cross in 9 seconds, so the relative speed is:

Converting to km/h:

Step 3: Apply the relative speed formula for trains moving towards each other

When two trains move towards each other:

where $v_1=40\text{km/h}$ (first train) and $v_2$ is unknown.

Step 4: Solve for the second train's speed

**Answer: The speed of the second train is $120\text{km/h}$ (Option A)**

CP = 1200 × $\frac{100}{120}$ = Rs. 1000

Net rate = $\frac{1}{15}$ - $\frac{1}{20}$ = $\frac{4}{60}$ - $\frac{3}{60}$ = $\frac{1}{60}$. Time = 60 hours

# Solution: Profit Calculation with Markup and Discount

Understanding profit requires calculating the selling price after applying markup and discount to the cost price.

Step 1: Calculate the Marked Price

The merchant marks goods 50% above the cost price of Rs. 8000.

Step 2: Calculate the Selling Price After Discount

A discount of 10% is given on the marked price of Rs. 12000.

Step 3: Calculate the Profit

Profit is the difference between selling price and cost price.

The merchant's profit is Rs. 2800.

Answer: (D) Rs. 2800 ✓

Net rate = $\frac{1}{20}$ + $\frac{1}{30}$ - $\frac{1}{40}$ = $\frac{6}{120}$ + $\frac{4}{120}$ - $\frac{3}{120}$ = $\frac{7}{120}$. Time = $\frac{120}{7}$ ≈ 17.14 minutes

Downstream speed = $\frac{72}{3}$ = 24 km/h. Upstream speed = $\frac{72}{6}$ = 12 km/h. Current = (24-12)/2 = 6 km/h

P(1.2)² = 14400. P × 1.44 = 14400. P = Rs. 10000

Work done in 3 days = 3($\frac{1}{12}$ + $\frac{1}{18}$) = 3($\frac{3}{36}$ + $\frac{2}{36}$) = 3 × $\frac{5}{36}$ = $\frac{5}{12}$. Remaining = $\frac{7}{12}$. Y completes $\frac{7}{12}$ in ($\frac{7}{12}$)/($\frac{1}{18}$) = $\frac{7}{12}$ × 18 = 10.5 days

Number = 45 × $\frac{100}{15}$ = 300. 40% of 300 = 300 × $\frac{40}{100}$ = 120

# Solution: Net Percentage Change After Two Operations

When a quantity undergoes successive percentage changes, we apply each change sequentially to find the overall effect.

Step 1: Represent the original number

Let the original number be $x$.

Step 2: Apply the 25% increase

After a 25% increase:

Step 3: Apply the 20% decrease

The decrease is applied to the new value $1.25x$, not the original:

Step 4: Calculate the net change

The final value equals the original value. Therefore:

Assume the original number is 100.

Increase by 25%:

100×1.25=125

Then decrease by 20%:

125×0.80=100

So, the final value is again 100.

Therefore, the net percentage change is 0%.

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

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Key Insight: A 25% increase followed by a 20% decrease does NOT cancel out to 0% by simple arithmetic (25 − 20 = 5). Instead, multiplying the multipliers $(1.25\times 0.80=1.00)$ gives the true result because the 20% decrease applies to the larger amount.

SP = CP + Profit = 500 + (35% of 500) = 500 + 175 = Rs. 675

A's work rate = $\frac{1}{20}$, B's work rate = $\frac{1}{30}$. Combined rate = $\frac{1}{20}$ + $\frac{1}{30}$ = $\frac{5}{60}$ = $\frac{1}{12}$. Time = 12 days

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

Time = Distance/Speed = $\frac{300}{60}$ = 5 hours

Speed of current = (Downstream speed - Upstream speed)/2 = (12 - 8)/2 = 2 km/h

SI = (5000 × 12 × 3)/100 = 1800. Amount = 5000 + 1800 = Rs. 6800