Quantitative Aptitude - MCQ Practice Questions

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)**

Profit = (1.40 × 0.90 - 1) × 100 = 1.26 - 1 = 0.26 = 26%

SI = (P × R × T)/100 = (8000 × 7.5 × 4)/100 = $\frac{240000}{100}$ = Rs. 2400

Net rate = $\frac{1}{12}$ + $\frac{1}{15}$ - $\frac{1}{20}$ = $\frac{5}{60}$ + $\frac{4}{60}$ - $\frac{3}{60}$ = $\frac{6}{60}$ = $\frac{1}{10}$. Time = 10 hours

100 × 1.20 × 0.90 = 108. Net increase = 8%

Let number = x. 0.60x = 240. x = $\frac{240}{0}$.60 = 400

Combined rate = $\frac{1}{20}$ + $\frac{1}{30}$ = $\frac{3}{60}$ + $\frac{2}{60}$ = $\frac{5}{60}$ = $\frac{1}{12}$. Time = 12 days

Amount = 10000 × (1.20)² = 10000 × 1.44 = Rs. 14400

Total distance = 60×2 + 40×3 = 120 + 120 = 240 km. Total time = 2 + 3 = 5 hours. Average speed = $\frac{240}{5}$ = 48 km/h

SP = 500 × 1.35 = Rs. 675

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%

Total distance = 180 + 320 = 500m. Speed = $\frac{500}{25}$ = 20 m/s = 20 × 3.6 = 72 km/h

Combined rate = $\frac{1}{10}$ + $\frac{1}{12}$ + $\frac{1}{15}$ = $\frac{6}{60}$ + $\frac{5}{60}$ + $\frac{4}{60}$ = $\frac{15}{60}$ = $\frac{1}{4}$. Time = 4 days

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)

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)**

Rate = $\frac{1}{12}$ + $\frac{1}{18}$ - $\frac{1}{36}$ = $\frac{3}{36}$ + $\frac{2}{36}$ - $\frac{1}{36}$ = $\frac{4}{36}$ = $\frac{1}{9}$. Time = 9 hours.

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