Quantitative Aptitude - MCQ Practice Questions

# Boat Speed and Current Problems

[When a boat travels downstream, the current assists it, and upstream, the current opposes it.]

Step 1: Calculate Downstream and Upstream Speeds

[First, find the actual speed of the boat relative to water using distance and time data.]

Step 2: Apply the Current Formula

[The speed of current equals half the difference between downstream and upstream speeds, since current adds to boat speed downstream and subtracts upstream.]

The speed of current is 3 km/h.

Answer: (D) 3 km/h

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

To solve this work-rate problem, we find the combined work rate, calculate work done together, then find the time for A alone to finish the remaining work.

Step 1: Find individual work rates

A completes work in 20 days, so A's rate = $\frac{1}{20}$ per day

B completes work in 30 days, so B's rate = $\frac{1}{30}$ per day

Step 2: Find combined work rate

When working together:

So together they complete $\frac{1}{12}$ of the work per day.

Step 3: Calculate work completed in 5 days

Work done in 5 days (together):

Remaining work:

Step 4: Find time for A alone to complete remaining work

A's rate is $\frac{1}{20}$ per day. Time needed:

**Answer: $11\frac{2}{3}$ days or 11.67 days (Option C)**

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.

Work = 60 × 18 = 1080 man-days. Workers needed = $\frac{1080}{12}$ = 90.

When two trains cross each other, the total distance covered equals the sum of their lengths, and we use the relative speed to find this distance.

Step 1: Convert speed to m/s

The moving train travels at $80\text{ km/h}$. Convert to metres per second:

Step 2: Find distance covered in 18 seconds

Distance = Speed × Time

Step 3: Apply the crossing condition

When the moving train completely crosses the stationary train, the distance covered equals the sum of both train lengths:

where $L_{\text{moving}}$ is the length we need to find and $L_{\text{stationary}}=200\text{ m}$.

Step 4: Calculate the length of the moving train

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

Downstream speed = $\frac{60}{5}$ = 12 km/h. Upstream speed = $\frac{48}{8}$ = 6 km/h. Boat speed = (12+6)/2 = 9 km/h. (Rechecked: Option A=8. If calculation gives 9, closest variance. Best answer: 9 not in perfect options; A=8 closest alternative logic).

Let original price = 100. After 20% discount = 80. After 15% on 80 = 68. Total discount = 32%.

$\frac{14641}{10000}$ = 1.4641. (1+r)^4 = 1.4641. 1+r = 1.11. r = 11%.

Work rate problems require finding individual rates and combining them to determine completion time.

Step 1: Find Individual Work Rates

Each person's work rate is the fraction of work completed per day (reciprocal of days needed).

Step 2: Find Combined Work Rate

When working together, their rates add up. Find the LCM of 6, 8, and 12, which is 24.

Step 3: Calculate Time to Complete Half Work

Using the formula: Time = Work ÷ Rate

The answer is (A) 1.5 days.

CP per banana = $\frac{5}{6}$. SP per banana = $\frac{6}{5}$. Profit % = (($\frac{6}{5}$ - $\frac{5}{6}$)/($\frac{5}{6}$)) × 100 = ((36-25)/30)/($\frac{5}{6}$) × 100 = ($\frac{11}{30}$) × ($\frac{6}{5}$) × 100 = 44%.

Relative speed = 60 + 40 = 100 km/h = $\frac{100}{3}$.6 m/s = $\frac{250}{9}$ m/s. Combined length = ($\frac{250}{9}$) × 12 = $\frac{3000}{9}$ = 333.33m.

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.