Comparing Quantities (Simple Interest) exercise - Free Printable

Explanation:
We’ll solve each question one by one using the Simple Interest formula:

> Simple Interest (SI) = (P × R × T) / 100
Where:
- P = Principal (initial amount)
- R = Rate of interest per annum (%)
- T = Time in years

Also, for problems asking when an amount doubles:
If amount doubles, then Interest = Principal, so:
SI = P ⇒ (P × R × T)/100 = P ⇒ R × T = 100 ⇒ T = 100/R or R = 100/T.

Let’s go step by step:

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1. P = ₹800, R = 18%, T = 1 year
SI = (800 × 18 × 1)/100 = 14400/100 = ₹144

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2. P = ₹4000, R = 15%, T = 5 years
SI = (4000 × 15 × 5)/100 = (4000 × 75)/100 = 300000/100 = ₹3000

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3. P = ₹750, Amount = ₹900 ⇒ SI = 900 − 750 = ₹150
R = 4%
We need T:
SI = (P × R × T)/100
150 = (750 × 4 × T)/100
150 = (3000 × T)/100
150 = 30 × T
⇒ T = 150 / 30 = 5 years

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4. Amount doubles ⇒ SI = P
So: (P × R × 8)/100 = P
Cancel P (P ≠ 0): (R × 8)/100 = 1
⇒ 8R = 100 ⇒ R = 100/8 = 12.5%

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5. P = ₹20,000, R = 9%
First, find time between 28 March 2000 and 21 August 2000.

Count days:
- March: 28 to 31 → 3 days (excluding 28? Wait — deposit on 28 March, so interest starts *from* 28 March. Usually, in simple interest, the day of deposit is included or excluded depending on convention. In school problems, we usually count full days between dates, but for simplicity in Class 7, they often use months as fractions of a year.

Let’s count months:
- March 28 → March has 31 days, so from 28 Mar to 31 Mar = 3 days
- April = 30
- May = 31
- June = 30
- July = 31
- Aug 1 to 21 = 21 days

Total days = 3 + 30 + 31 + 30 + 31 + 21 = 146 days

Now convert to years: 146 / 365 ≈ 0.4 years (but many textbooks use 360 days/year for simplicity — however, since it's not specified, and it's a school worksheet, let’s check if exact fraction works nicely).

Alternatively, maybe they expect approximate:
From 28 March to 21 Aug is about 4 months and 24 days ≈ 4.8 months ≈ 4.8/12 = 0.4 years.

But better: Let’s compute exactly with 365 days.

T = 146/365 years
SI = (20000 × 9 × 146)/(100 × 365)
= (20000 × 9 × 146) / 36500
Simplify: 20000 / 100 = 200
So: SI = (200 × 9 × 146) / 365
= (1800 × 146) / 365
1800/365 = 360/73
So: (360 × 146) / 73
Note: 146 = 2 × 73
So: (360 × 2 × 73) / 73 = 360 × 2 = ₹720

✔ Nice! So interest = ₹720
Amount = P + SI = 20,000 + 720 = ₹20,720

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6. P = ₹1000, R = 5% per annum, but time = 6 months = 0.5 year
SI = (1000 × 5 × 0.5)/100 = (2500)/100 = ₹25

*(Note: “5 paise per rupee per month” means 5 paise interest per ₹1 per month = 5% per month? Wait — careful!)*

Hold on — re-read Q6:
> “Find the simple interest on ₹1000 for 6 months at the rate of 5 paise per rupee per month?”

Ah! This is not 5% per annum — it's 5 paise per rupee per month.

That means:
For every ₹1, interest per month = 5 paise = ₹0.05
So for ₹1000, interest per month = 1000 × 0.05 = ₹50
For 6 months: 50 × 6 = ₹300

Yes! That’s the correct interpretation. The phrase “5 paise per rupee per month” is a rate per month, not per annum.

So answer = ₹300

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7. P = ₹400, R = 5% per annum, T = 2 years
SI = (400 × 5 × 2)/100 = 4000/100 = ₹20

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8. P = ₹25,000, R = 8%, T = 6 years
SI = (25000 × 8 × 6)/100 = (25000 × 48)/100 = 1,200,000 / 100 = ₹12,000

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9. Amount doubles in 10 years ⇒ SI = P
So: (P × R × 10)/100 = P
⇒ (10R)/100 = 1
⇒ R = 100/10 = 10%

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10. P = ₹8000, Amount = ₹8360 ⇒ SI = 8360 − 8000 = ₹360
R = 6% per annum
Find T (in years), then convert to months.

SI = (P × R × T)/100
360 = (8000 × 6 × T)/100
360 = (48000 × T)/100
360 = 480 × T
⇒ T = 360 / 480 = 0.75 years
0.75 × 12 = 9 months

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Now collect all answers:

1. ₹144
2. ₹3000
3. 5 years
4. 12.5%
5. ₹20,720
6. ₹300
7. ₹20
8. ₹12,000
9. 10%
10. 9 months

Final Answer:
1. 144
2. 3000
3. 5
4. 12.5
5. 20720
6. 300
7. 20
8. 12000
9. 10
10. 9