State PSC Exam Preparation — BPSC, UPPSC, MPPSC

Q.11 Easy

A sum of money becomes ₹9,600 after 5 years at a simple interest rate of 8% per annum. What was the principal amount?

A₹6,000

B₹6,857

C₹7,200

D₹8,000

Correct Answer: A. ₹6,000

Explanation:

Step 1: Identify the Simple Interest Formula

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

A = P + \frac{PRT}{100}

Step 2: Substitute Known Values

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

9,600 = P + \frac{P \times 8 \times 5}{100}

Step 3: Simplify and Solve for Principal

9,600 = P + \frac{40P}{100}

\[9,600 = P + 0.4P\]

\[9,600 = 1.4P\]

P = \frac{9,600}{1.4} = \frac{96,000}{14} = 6,000

The principal amount was ₹6,000.

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Q.12 Medium

The simple interest on a certain sum for 3 years at 12% per annum is ₹3,600. If the same sum is invested for 5 years at 10% per annum, what will be the simple interest earned?

A₹4,000

B₹5,000

C₹6,000

D₹7,200

Correct Answer: B. ₹5,000

Explanation:

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

3,600 = \frac{P \times 12 \times 3}{100}

Step 2: Solve for Principal

3,600 = \frac{36P}{100}

P = \frac{3,600 \times 100}{36} = \frac{360,000}{36} = ₹10,000

Step 3: Calculate Simple Interest for New Investment

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

SI = \frac{P \times R \times T}{100} = \frac{10,000 \times 10 \times 5}{100}

SI = \frac{500,000}{100} = ₹5,000

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

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Q.13 Easy

A person invests ₹5,000 at 6% per annum simple interest. After how many years will the amount become ₹6,500?

A3 years

B4 years

C5 years

D6 years

Correct Answer: C. 5 years

Explanation:

Step 1: Identify the given values

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

P = 5000, \quad R = 6\%, \quad A = 6500

Step 2: Calculate the Simple Interest

Simple Interest (SI) = Final Amount - Principal

\[SI = A - P = 6500 - 5000 = 1500\]

Step 3: Apply the Simple Interest formula to find Time

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

1500 = \frac{5000 \times 6 \times T}{100}

1500 = \frac{30000 \times T}{100}

1500 = 300 \times T

T = \frac{1500}{300} = 5 \text{ years}

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

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Q.14 Hard

Two sums of money are in the ratio 3:5. They are invested at simple interest rates of 8% and 6% per annum respectively. After 4 years, the difference in their simple interests is ₹480. What are the two principal amounts?

A₹1,500 and ₹2,500

B₹2,400 and ₹4,000

C₹3,000 and ₹5,000

D₹3,600 and ₹6,000

Correct Answer: C. ₹3,000 and ₹5,000

Explanation:

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.

\text{Principal}_1 = 3x, \quad \text{Principal}_2 = 5x

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:

SI_1 = \frac{3x \times 8 \times 4}{100} = \frac{96x}{100} = 0.96x

For the second principal at 6% per annum:

SI_2 = \frac{5x \times 6 \times 4}{100} = \frac{120x}{100} = 1.2x

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

The difference in simple interests is ₹480.

\[SI_2 - SI_1 = 480\]

\[1.2x - 0.96x = 480\]

\[0.24x = 480\]

x = \frac{480}{0.24} = 2000

Step 4: Calculate the two principal amounts

Substitute x = 2000 into the principal expressions.

\text{Principal}_1 = 3x = 3 \times 2000 = ₹3,000

\text{Principal}_2 = 5x = 5 \times 2000 = ₹5,000

**The two principal amounts are ₹3,000

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Q.15 Medium

A sum becomes 4 times itself in 15 years at simple interest. What is the rate of interest per annum?

A15%

B18%

C20%

D25%

Correct Answer: C. 20%

Explanation:

Step 1: Identify the Simple Interest Formula

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

A = P + SI \text{ where } SI = \frac{P \times R \times T}{100}

Step 2: Set up the equation using given information

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

\[4P = P + SI\]

\[SI = 4P - P = 3P\]

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

3P = \frac{P \times R \times 15}{100}

3P = \frac{15PR}{100}

3 = \frac{15R}{100}

R = \frac{3 \times 100}{15} = \frac{300}{15} = 20\%

The rate of interest per annum is 20%.

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Q.16 Easy Profit and Loss

A trader buys mangoes at ₹8 per kg and sells them at ₹12 per kg. What is his profit percentage?

A40%

B50%

C60%

D45%

Correct Answer: B. 50%

Explanation:

Step 1: Identify Cost Price and Selling Price

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

\text{CP} = ₹8, \quad \text{SP} = ₹12

Step 2: Calculate Profit

Profit = Selling Price − Cost Price

\text{Profit} = ₹12 - ₹8 = ₹4

Step 3: Calculate Profit Percentage

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

\text{Profit\%} = \frac{\text{Profit}}{\text{Cost Price}} \times 100 = \frac{4}{8} \times 100 = \frac{1}{2} \times 100 = 50\%

The trader's profit percentage is 50%.

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Q.17 Easy Profit and Loss

If an article is purchased for ₹450 and sold at a loss of 8%, what is the selling price?

A₹414

B₹418

C₹420

D₹422

Correct Answer: A. ₹414

Explanation:

Step 1: Identify the given information

Cost Price (CP) = ₹450 and Loss = 8%

\text{Given: CP} = ₹450, \text{ Loss} = 8\%

Step 2: Calculate the loss amount

Loss amount = 8% of Cost Price

\text{Loss amount} = \frac{8}{100} \times 450 = 0.08 \times 450 = ₹36

Step 3: Calculate the selling price

Selling Price = Cost Price − Loss amount

\text{SP} = 450 - 36 = ₹414

The selling price of the article is ₹414.

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Q.18 Medium Profit and Loss

A shopkeeper marks an article at ₹500 and gives a discount of 20%. If he still makes a profit of 25%, what was the cost price?

A₹315

B₹320

C₹325

D₹330

Correct Answer: B. ₹320

Explanation:

Step 1: Calculate the Selling Price after discount

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

\text{Selling Price} = 500 - (20\% \text{ of } 500) = 500 - \frac{20}{100} \times 500

\[= 500 - 100 = ₹400\]

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.

\text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{Profit\%}}{100}\right)

400 = \text{Cost Price} \times \left(1 + \frac{25}{100}\right)

400 = \text{Cost Price} \times 1.25

Step 3: Solve for Cost Price

\text{Cost Price} = \frac{400}{1.25} = \frac{400}{\frac{5}{4}} = 400 \times \frac{4}{5}

= \frac{1600}{5} = ₹320

The cost price of the article is ₹320.

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Q.19 Hard Profit and Loss

A merchant sold two items for ₹2,000 each. On one item he made 25% profit and on the other he made 25% loss. What is his overall profit or loss percentage?

A6.25% profit

B6.25% loss

CNo profit, no loss

D5% loss

Correct Answer: B. 6.25% loss

Explanation:

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

2000 = CP_1 \times 1.25

CP_1 = \frac{2000}{1.25} = \frac{2000}{\frac{5}{4}} = 2000 \times \frac{4}{5} = 1600

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

2000 = CP_2 \times 0.75

CP_2 = \frac{2000}{0.75} = \frac{2000}{\frac{3}{4}} = 2000 \times \frac{4}{3} = 2666.67

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

\text{Loss} = CP - SP = 4266.67 - 4000 = 266.67

\text{Loss\%} = \frac{\text{Loss}}{\text{Total CP}} \times 100 = \frac{266.67}{4266.67} \times 100 = 6.25\%

**The merchant made an overall loss of 6.

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Q.20 Easy Profit and Loss

A retailer buys notebooks at ₹40 each and sells them at ₹50 each. How many notebooks must he sell to make a profit of ₹600?

A55

B60

C65

D70

Correct Answer: B. 60

Explanation:

Step 1: Find profit per notebook

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

\text{Profit per notebook} = 50 - 40 = ₹10

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.

\text{Total Profit} = \text{Profit per notebook} \times \text{Number of notebooks}

600 = 10 \times x

Step 3: Solve for number of notebooks

Divide both sides by 10 to find x.

x = \frac{600}{10} = 60

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

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