💰 Simple Interest: Two Amounts Concept with Questions

In Simple Interest, when you’re given two different amounts at different times, you can calculate SI per year, Principal, or Rate using the formula:

\[ A_m - A_n = SI_1 \times (m - n) \]

Let’s explore this through practical examples.

📌 Question 1 :
Two grocers invested the same amount. After 5 years, one received Rs1600. After 7 years, the other received Rs2000. What is the rate of interest per annum?

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\[ A_7 - A_5 = 2000 - 1600 = 400 \Rightarrow SI_2 = 400 \Rightarrow SI_1 = 200 \] \[ SI_5 = 200 \times 5 = 1000 \Rightarrow P = 1600 - 1000 = 600 \] \[ SI_7 = 200 \times 7 = 1400 \Rightarrow R = \frac{1400 \times 100}{600 \times 7} = \boxed{33.33\%} \]

📌 Question 2 :
The amount becomes Rs4000 in 4 years and Rs4600 in 8 years. Find the principal and rate of interest.

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\[ A_8 - A_4 = 4600 - 4000 = 600 \Rightarrow SI_4 = 600 \Rightarrow SI_1 = 150 \] \[ SI_4 = 150 \times 4 = 600 \Rightarrow P = 4000 - 600 = \boxed{Rs 3400} \] \[ R = \frac{150 \times 100}{3400} = \boxed{4.41\%} \]

📌 Question 3 :
A sum amounts to Rs1600 in 5 years and Rs2000 in 9 years. Find the principal and rate of interest.

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\[ A_9 - A_5 = 2000 - 1600 = 400 \Rightarrow SI_4 = 400 \Rightarrow SI_1 = 100 \] \[ SI_5 = 100 \times 5 = 500 \Rightarrow P = 1600 - 500 = \boxed{Rs1100} \] \[ R = \frac{100 \times 100}{1100} = \boxed{9.09\%} \]

📌 Question 4 :
If the principal is Rs3640 and simple interest per year is Rs40, what is the amount after 6 and 10 years?

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\[ SI_6 = 40 \times 6 = 240 \Rightarrow A_6 = 3640 + 240 = \boxed{Rs3880} \] \[ SI_{10} = 40 \times 10 = 400 \Rightarrow A_{10} = 3640 + 400 = \boxed{Rs4040} \]