Quantitative Aptitude - MCQ Practice Questions

Step 1: Calculate the original speed

The train travels 240 km in 4 hours, so we divide distance by time.

Step 2: Calculate the new speed after 20% increase

The speed increases by 20%, so we multiply the original speed by 1.20.

Step 3: Calculate distance covered in 5 hours at new speed

Distance equals speed multiplied by time.

The train will cover 360 km in 5 hours at the new speed.

Step 1: Define Variables and Set Up Equations

Let the distance between A and B be $d$ km. Time to go from A to B at 4 km/h is $\frac{d}{4}$ hours, and time to return from B to A at 6 km/h is $\frac{d}{6}$ hours.

Step 2: Find Common Denominator and Simplify

The common denominator of 4 and 6 is 12. Rewrite each fraction with denominator 12.

Step 3: Solve for Distance

Combine the fractions on the left side and solve for $d$.

The distance between A and B is 12 km.

Step 1: Find the downstream speed

The boat travels 120 km downstream in 6 hours.

Step 2: Find the upstream speed

The boat travels 120 km upstream in 8 hours.

Step 3: Calculate the speed of boat in still water

The speed of boat in still water is the average of downstream and upstream speeds.

The speed of the boat in still water is 17.5 km/h.

Step 1: Define Variables and Total Distance

Let the total distance be $D$ km. The car travels $\frac{D}{2}$ km at each speed.

Step 2: Calculate Time for Each Half

For the first half at 60 km/h:

For the second half at 90 km/h:

Step 3: Calculate Total Time and Average Speed

Total time for the journey:

Average speed is total distance divided by total time:

The average speed for the entire journey is 72 km/h.

Step 1: Calculate Total Cost Price

The shopkeeper buys 120 notebooks at ₹40 each.

Step 2: Calculate Total Selling Price

The shopkeeper sells 120 notebooks at ₹50 each.

Step 3: Calculate Total Profit

Profit is the difference between selling price and cost price.

The shopkeeper's total profit for selling 120 notebooks in a day is ₹1,200.

Step 1: Calculate the Marked Price

The marked price is 60% above the cost price of ₹800.

Step 2: Calculate the Selling Price

A discount of 20% is offered on the marked price of ₹1280.

Step 3: Calculate the Profit Percentage

The profit is the difference between selling price and cost price, divided by cost price and multiplied by 100.

The trader made a profit of 28% on the watch.

Step 1: Cost price of the article sold at 25% profit

Since $S{P}_1=\text{₹}1000$ at a 25% profit:

Step 2: Cost price of the article sold at 25% loss

Since $S{P}_2=\text{₹}1000$ at a 25% loss:

Step 3: Overall profit or loss

Since $\text{Total CP}=\frac{6400}{3}\approx 2133.33>2000=\text{Total SP}$, there is a loss:

Quick formula: Whenever two items are sold at the same price, one at $x\%$ profit and the other at $x\%$ loss, there is always a net loss given by:

Step 1: Calculate Total Cost Price

The merchant's total cost includes the purchase price, transportation, and packaging costs.

Step 2: Calculate Profit Amount

The merchant wants to make a 20% profit on the total cost price.

Step 3: Calculate Selling Price

The selling price is the total cost price plus the profit amount.

The merchant should sell the goods at ₹21,000 to make a 20% profit.

To find the required selling price, we need to work backwards from the desired overall profit.

Step 1: Calculate Selling Price of Item A

Item A is sold at 15% profit on its cost price of ₹4,000.

Step 2: Calculate Total Cost Price and Required Total Selling Price

The total cost price of both items combined is the sum of individual cost prices.

For an overall profit of 5%, the total selling price should be:

Step 3: Find Required Selling Price of Item B

Since Total Selling Price = Selling Price of A + Selling Price of B:

The selling price of Item B should be ₹5,900.

Cost price of Item A =₹4,000

Sold at 15% profit:

SP

A

​

=4000+15% of 4000

=4000+600=₹4600

Cost price of Item B =₹6,000

Total cost price:

4000+6000=₹10,000

For an overall profit of 5%:

Required total selling price=10000+5% of 10000

=10000+500=₹10,500

Therefore, required selling price of Item B:

SP

B

​

=10500−4600

=₹5900

So, the selling price of Item B should be:

₹5,900

​

Answer: (B) 5900

Step 1: Identify the Simple Interest Formula

The formula for amount in simple interest is A = P + SI, where SI = PRT/100

Step 2: Substitute Known Values

Given: A = ₹9,600, T = 5 years, R = 8% per annum

Step 3: Simplify and Solve for Principal

The principal amount was ₹6,000.

Step 1: Find the Principal using Simple Interest Formula

Using the formula SI = PRT/100, where SI = ₹3,600, R = 12% p.a., T = 3 years

Step 2: Solve for Principal

Step 3: Calculate Simple Interest for New Investment

For P = ₹10,000, R = 10% p.a., T = 5 years

The simple interest earned on ₹10,000 invested for 5 years at 10% per annum is ₹5,000.

Step 1: Identify the given values

Principal (P) = ₹5,000, Rate (R) = 6% per annum, Final Amount (A) = ₹6,500

Step 2: Calculate the Simple Interest

Simple Interest (SI) = Final Amount - Principal

Step 3: Apply the Simple Interest formula to find Time

Using the formula: $SI=\frac{P\times R\times T}{100}$

The amount will become ₹6,500 after 5 years.

Step 1: Set up the principal amounts using the ratio

Let the two principal amounts be 3x and 5x respectively, since they are in the ratio 3:5.

Step 2: Calculate simple interest for both principals

Using the formula SI = (P × R × T)/100, calculate interest for each principal over 4 years.

For the first principal at 8% per annum:

For the second principal at 6% per annum:

Step 3: Find the difference in simple interests and solve for x

The difference in simple interests is ₹480.

Step 4: Calculate the two principal amounts

Substitute x = 2000 into the principal expressions.

**The two principal amounts are ₹3,000

Step 1: Identify the Simple Interest Formula

Let Principal = P, Amount = A, Rate = R% per annum, Time = T years

Step 2: Set up the equation using given information

Given that the sum becomes 4 times itself, so Amount = 4P

Step 3: Substitute into Simple Interest formula and solve for rate

The rate of interest per annum is 20%.

Step 1: Identify Cost Price and Selling Price

Cost Price (CP) = ₹8 per kg and Selling Price (SP) = ₹12 per kg

Step 2: Calculate Profit

Profit = Selling Price − Cost Price

Step 3: Calculate Profit Percentage

Profit percentage is calculated as profit divided by cost price, multiplied by 100

The trader's profit percentage is 50%.

Step 1: Identify the given information

Cost Price (CP) = ₹450 and Loss = 8%

Step 2: Calculate the loss amount

Loss amount = 8% of Cost Price

Step 3: Calculate the selling price

Selling Price = Cost Price − Loss amount

The selling price of the article is ₹414.

Step 1: Calculate the Selling Price after discount

The marked price is ₹500 and discount is 20%.

Step 2: Use the profit formula to find Cost Price

The shopkeeper makes a profit of 25%, which means Selling Price is 125% of Cost Price.

Step 3: Solve for Cost Price

The cost price of the article is ₹320.

Step 1: Find the Cost Price of the first item (25% profit)

If selling price is ₹2,000 with 25% profit, then SP = CP × 1.25

Step 2: Find the Cost Price of the second item (25% loss)

If selling price is ₹2,000 with 25% loss, then SP = CP × 0.75

Step 3: Calculate overall profit or loss percentage

Total Cost Price = ₹1,600 + ₹2,666.67 = ₹4,266.67

Total Selling Price = ₹2,000 + ₹2,000 = ₹4,000

**The merchant made an overall loss of 6.

Step 1: Find profit per notebook

The retailer buys at ₹40 and sells at ₹50, so profit on each notebook is the difference.

Step 2: Set up equation for total profit

Let the number of notebooks sold be x. The total profit equals profit per notebook multiplied by number of notebooks.

Step 3: Solve for number of notebooks

Divide both sides by 10 to find x.

The retailer must sell 60 notebooks to make a profit of ₹600.

Step 1: SP at 20% loss = ₹1200, so CP = $\frac{1200}{0}$.80 = ₹1500.

Step 2: For 20% profit: New SP = CP × (1 + $\frac{20}{100}$) = 1500 × 1.20 = ₹1800.

So option B is correct.