Simple Interest worksheet for Class 8 students, featuring problems on calculating interest, time, and rates, with multiple-choice and fill-in-the-blank questions.

Here's the complete solution to all the questions in the worksheet, explained step by step.

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(1) Priyanka borrowed Rs.25920 from Ridhima at the rate of 8% simple interest per year. She then returned the money after 3 years and 2 months. How much money did she give to Ridhima in total?

Given:
- Principal (P) = Rs. 25920
- Rate (R) = 8% per annum
- Time (T) = 3 years 2 months = 3 + 2/12 = 3 + 1/6 = 19/6 years

Formula for Simple Interest (SI):
> SI = (P × R × T) / 100

Calculate SI:
SI = (25920 × 8 × 19) / (100 × 6)
= (25920 × 152) / 600
First, simplify:
25920 ÷ 600 = 43.2 → 43.2 × 152 = ?

Better to compute directly:

25920 × 8 = 207360
207360 × 19 = 3,939,840
Now divide by 600:
3,939,840 ÷ 600 = 6566.4

So, SI = Rs. 6566.40

Total amount to be returned = P + SI = 25920 + 6566.40 = Rs. 32486.40

✔ Answer: Rs. 32486.40

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(2) Iqbal deposited an amount in bank which gives 5% simple interest. If he gets Rs.75000 after 10 years, find the amount deposited by him?

Given:
- Amount (A) = Rs. 75000
- Rate (R) = 5% per annum
- Time (T) = 10 years

We know:
> A = P + SI = P + (P×R×T)/100 = P(1 + RT/100)

So,
75000 = P × (1 + (5×10)/100) = P × (1 + 0.5) = P × 1.5

Therefore,
P = 75000 / 1.5 = Rs. 50000

✔ Answer: Rs. 50000

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(3) A sum of money becomes 5 times of itself at simple interest in 28 years, how long would it take for same amount to become double?

Let principal = P

After 28 years, amount = 5P → So, SI = 5P - P = 4P

Use formula:
SI = (P × R × T)/100

→ 4P = (P × R × 28)/100

Cancel P from both sides:
4 = (R × 28)/100

→ R = (4 × 100) / 28 = 400 / 28 = 100 / 7 ≈ 14.2857%

Now, we want time (T) for amount to become double → SI = 2P - P = P

So,
P = (P × R × T)/100

Cancel P:
1 = (R × T)/100 → T = 100 / R = 100 / (100/7) = 7 years

✔ Answer: 7 years

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(4) Sunil deposited Rs. 300 in bank on 15th November 2003 and withdrew on 15th February 2004. Find the interest earned by him at simple interest of 36% pa.

Time period:
From 15 Nov 2003 to 15 Feb 2004 = 3 months

Because:
- Nov 15 to Dec 15 = 1 month
- Dec 15 to Jan 15 = 1 month
- Jan 15 to Feb 15 = 1 month

So, T = 3 months = 3/12 = 1/4 year

Given:
P = Rs. 300
R = 36% pa
T = 1/4 year

SI = (P × R × T)/100 = (300 × 36 × 1/4) / 100

First, 300 × 36 = 10800
Then, 10800 × 1/4 = 2700
Then, 2700 / 100 = Rs. 27

✔ Answer: Rs. 27

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(5) The simple interest of Rs.24000 in 3 years at 4% per annum will be same as simple interest on Rs.7200 at 5% per annum in how many years?

First, calculate SI on Rs.24000 at 4% for 3 years:

SI₁ = (24000 × 4 × 3) / 100 = (24000 × 12) / 100 = 288000 / 100 = Rs. 2880

Now, let time for Rs.7200 at 5% be T years, such that SI₂ = 2880

SI₂ = (7200 × 5 × T) / 100 = 2880

→ (36000 × T) / 100 = 2880
→ 360 × T = 2880
→ T = 2880 / 360 = 8 years

✔ Answer: 8 years

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(6) What should be the interest rate for an amount to become double of itself at simple interest in 25 years?

Amount becomes double → SI = P

SI = (P × R × T)/100 = P

→ (P × R × 25)/100 = P

Cancel P:
(R × 25)/100 = 1
→ R = 100 / 25 = 4% pa

✔ Answer: b. 4% pa

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(7) How long will it take for an amount to become 5 times of itself at 5% per annum simple interest?

Amount = 5P → SI = 4P

SI = (P × R × T)/100 = 4P

→ (P × 5 × T)/100 = 4P

Cancel P:
(5T)/100 = 4
→ T = (4 × 100) / 5 = 400 / 5 = 80 years

✔ Answer: a. 80 years

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(8) Fill in the blanks: The simple interest of Rs.48000 in 5 years at 2% per annum will be same as simple interest on Rs.6000 at ___% per annum in 8 years.

First, calculate SI on Rs.48000 at 2% for 5 years:

SI = (48000 × 2 × 5) / 100 = (48000 × 10) / 100 = 480000 / 100 = Rs. 4800

Now, let rate be R% for Rs.6000 for 8 years to get same SI = 4800

SI = (6000 × R × 8) / 100 = 4800

→ (48000 × R) / 100 = 4800
→ 480 × R = 4800
→ R = 4800 / 480 = 10

✔ Answer: 10%

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## ✔ Final Answers Summary:

(1) Rs. 32486.40
(2) Rs. 50000
(3) 7 years
(4) Rs. 27
(5) 8 years
(6) b. 4% pa
(7) a. 80 years
(8) 10%

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