Quantitative Aptitude - MCQ Practice Questions

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: 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.

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 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: 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: 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.

Step 1: Let CP of 1 pen = ₹1.

Then CP of 12 pens = ₹12.

Step 2: SP of 10 pens = ₹12, so SP of 1 pen = ₹1.20.

Step 3: Profit% = [(1.20 - 1)/1] × 100 = 20%.

So option B is correct.

1. Calculate Total Cost Price (CP):The shopkeeper bought $100\text{ kg}$ of sugar at $₹20$ per kg.

2. Calculate Total Selling Price (SP):The shopkeeper sold the sugar in two batches:First batch: $60\text{ kg}$ at $₹25$ per kg.

Second batch: $40\text{ kg}$ at $₹18$ per kg.

3. Calculate Profit or Loss:Since the Total SP ($₹2220$) is greater than the Total CP ($₹2000$), the shopkeeper made a profit.

The shopkeeper made an overall profit of $₹220$.

In simple interest problems, the difference in amounts over different time periods reveals the interest earned, which we can use to find the principal and rate.

Step 1: Find the interest earned between the two periods

The amount after 2 years is ₹7,200 and after 3.5 years is ₹8,400.

Step 2: Calculate the annual simple interest rate

Since ₹1,200 is earned in 1.5 years, the annual interest is:

Step 3: Find the principal using the first condition

Using the simple interest formula: $A=P+I$, where $A$ is the amount, $P$ is the principal, and $I$ is total interest.

After 2 years:

Step 4: Verify with the second condition

After 3.5 years, total interest = $800\times 3.5=₹2,800$

Amount = $5,600+2,800=₹8,400$ ✓

Answer: The principal amount is ₹5,600 (Option D)

To find out who earned more interest, we calculate the simple interest for both Suresh and Amit using the formula:

1. Calculate Suresh's Interest:Principal ($P$) = ₹15,000Rate ($R$) = $7\%$Time ($T$) = $1.5$ years

2. Calculate Amit's Interest:Principal ($P$) = ₹12,000Rate ($R$) = $9\%$Time ($T$) = $2$ years

3. Comparison:Amit's interest: ₹2160Suresh's interest: ₹1575Since $₹2160>₹1575$, Amit earned more interest.

Amit earned more interest, by ₹585.

Simple interest is calculated as a percentage of the principal amount and remains constant each year, making it easier to compare different investment schemes.

Step 1: Calculate Maturity Amount for Scheme A

For Scheme A, we apply the simple interest formula where Principal = ₹20,000, Rate = 6% per annum, and Time = 4 years.

Step 2: Calculate Maturity Amount for Scheme B

For Scheme B, we apply the simple interest formula where Principal = ₹20,000, Rate = 5.5% per annum, and Time = 5 years.

Step 3: Compare the Maturity Amounts

To find which scheme is better and by how much, we subtract the smaller amount from the larger amount.

Since ₹25,500 > ₹24,800, Scheme B gives ₹700 more than Scheme A.

The answer is (C) Scheme B gives ₹700 more than Scheme A.

When interest is compounded semi-annually, the rate and time period must be adjusted accordingly. Use the compound interest formula $A=P{\left(1+\frac{r}{100}\right)}^n$ where $n$ represents the total number of compounding periods.

Step 1: Identify the given values and adjust for semi-annual compounding

Given:

For semi-annual compounding:

Step 2: Apply the compound interest formula

where $r=5\%$ and $n=4$:

Step 3: Simplify the expression

**Step 4: Calculate $(1.05{)}^4$** and find the final amount

Answer: The final amount is ₹14,586.08 (Option D)

For compound interest compounded half-yearly, we use the formula $A=P{\left(1+\frac{r}{100\times 2}\right)}^n$, where $n$ is the number of half-yearly periods.

Step 1: Identify the given values

Since interest is compounded half-yearly:

Step 2: Apply the compound interest formula

**Step 3: Calculate $(1.06{)}^3$

Step 4: Find the final amount and interest earned

Answer: Rakesh will earn ₹1,432.62 in compound interest (Option D)

Step 1: Let marked price = MP.

After 12% discount, SP = 0.88 × MP.

Step 2: 0.88 × MP = 275, so MP = $\frac{275}{0}$.88 = ₹312.50.

So option B is correct.

Step 1: Marked Price = 5,000 + 40% of 5,000 = 5,000 × 1.40 = ₹7,000.

Step 2: Selling Price = 7,000 - 15% of 7,000 = 7,000 × 0.85 = ₹5,950.

Step 3: Profit% = (5,950 - 5,000)/5,000 × 100 = $\frac{950}{5}$,000 × 100 = 19%.

So option B is correct.

Step 1: Let SP of each article = ₹100.

For first: CP₁ = $\frac{100}{1}$.25 = ₹80.

For second: CP₂ = $\frac{100}{0}$.75 = ₹133.33.

Step 2: Total CP = 80 + 133.33 = ₹213.33, Total SP = 200.

Step 3: Loss% = (213.33 - 200)/213.33 × 100 = 6.25%.

So option A is correct.

Step 1: Cost Price per lemon = $\frac{1}{5}$ = ₹0.20.

Selling Price per lemon = $\frac{1}{4}$ = ₹0.25.

Step 2: Profit per lemon = 0.25 - 0.20 = ₹0.05.

Step 3: Profit% = (0.$\frac{05}{0}$.20) × 100 = 25%.

So option B is correct.