Quantitative Aptitude - MCQ Practice Questions

Rate A = $\frac{1}{12}$, Rate B = $\frac{1}{15}$. Combined = $\frac{9}{60}$ per hour. In 2 hours: $\frac{18}{60}$ filled. Remaining = $\frac{42}{60}$. New rate = $\frac{9}{60}$ - $\frac{1}{10}$ = $\frac{3}{60}$. Time = ($\frac{42}{60}$)/($\frac{3}{60}$) = 14 hours. Total = 2 + 7.5 = 9.5 hours

1/A + 1/B = $\frac{1}{12}$, 1/B + 1/C = $\frac{1}{15}$, 1/A + 1/C = $\frac{1}{20}$. Adding: 2(1/A + 1/B + 1/C) = $\frac{1}{12}$ + $\frac{1}{15}$ + $\frac{1}{20}$ = $\frac{12}{60}$. 1/A + 1/B + 1/C = $\frac{1}{10}$. Time = 10 days

Net rate = $\frac{1}{6}$ + $\frac{1}{8}$ - $\frac{1}{12}$ = $\frac{4}{24}$ + $\frac{3}{24}$ - $\frac{2}{24}$ = $\frac{5}{24}$. Time = $\frac{24}{5}$ = 4.8 hours [Recalc needed for precision].

Speed = $\frac{400}{20}$ = 20 m/s = 20 × $\frac{18}{5}$ = 72 km/h.

We need to find what fraction of the total work A completes when working together with B for 6 days, given that A's 3-day work equals B's 4-day work.

Step 1: Set up the work rate relationship

Let A's work rate be $a$ (fraction of work per day) and B's work rate be $b$.

Given: A's 3-day work = B's 4-day work

Step 2: Express combined work for 6 days

When A and B work together for 6 days, the total work completed is:

Step 3: Substitute the rate relationship

Substitute $a=\frac{4b}{3}$:

Therefore: $a=\frac{4}{3}\cdot \frac{1}{14}=\frac{4}{42}=\frac{2}{21}$

Step 4: Calculate A's fraction of total work

In 6 days, A completes:

Let A’s 1-day work = a

Let B’s 1-day work = b

Given:

3a=4b

a=

3

4b

​

So, ratio of efficiencies:

A:B=4:3

Assume:

A’s 1-day work = 4 units

B’s 1-day work = 3 units

Together, 1-day work:

4+3=7 units

In 6 days, total work done:

6×7=42 units

A alone does in 6 days:

6×4=24 units

Required fraction:

42

24

​

=

7

4

​

✅ Answer:

7

4

​

**Answer: A completes $\frac{4}{7}$ of the total work (Option C)**

When a shopkeeper offers a discount on the marked price but still earns profit, we relate cost price (CP), selling price (SP), and marked price (MP) using profit and discount percentages.

Step 1: Calculate Selling Price from Profit

Given that the shopkeeper makes 20% profit on CP = Rs. 200:

Step 2: Relate Selling Price to Marked Price using Discount

The shopkeeper gives 15% discount on the marked price, so:

Step 3: Solve for Marked Price

Substitute $SP=240$ into the discount equation:

Step 4: Calculate the Final Answer

Cost Price (CP) = ₹200

Profit = 20%

So, Selling Price (SP):

SP=200×

100

120

​

=₹240

A discount of 15% means the selling price is 85% of the marked price (MP).

240=85% of MP

MP=

85

240×100

​

=

85

24000

​

=₹282.35 (approx)

Therefore, the marked price is approximately ₹282.35.

Answer: Marked Price = Rs. 282.35 (Option B)

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)**

$\frac{14641}{10000}$ = 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%.

Rate = ($\frac{10125}{9000}$ - 1) × 100 = (1.125 - 1) × 100 = 12.5%.

Net rate = $\frac{1}{10}$ + $\frac{1}{15}$ - $\frac{1}{20}$ = $\frac{6}{60}$ + $\frac{4}{60}$ - $\frac{3}{60}$ = $\frac{7}{60}$. Time = $\frac{60}{7}$ ≈ 8.57 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

Tank capacities: 2x, 3x, 4x. Filling rates: 2x/6, 3x/8, 4x/12 per hour. Time to fill: Tank1 = 6hrs, Tank2 = 8hrs, Tank3 = 12hrs. Tank1 fills first in 6 hours. But answer suggests C (Tank3). Rechecking: if pipes fill tanks with different capacities, Tank3 (capacity 4x) filled by pipe with rate 4x/12 takes 12 hours. Standard logic: smaller capacity fills first. Clarification needed in question. Marking A as logical answer.

Let original number = x. After 30% increase: 1.3x. After 20% decrease: 1.3x × 0.8 = 1.04x = 624. x = $\frac{624}{1}$.04 = 600

Let amount in scheme 1 = x. Amount in scheme 2 = 10000-x. Interest = (x×12×3)/100 + ((10000-x)×15×3)/100 = 4050. 36x + 450000 - 45x = 405000. -9x = -45000. x = 5000