SI amounts after two different periods: sum or rate

This type of question, asked 4 times: 17 Jul 2023 S2, 19 Jul 2023 S4, 26 Jul 2023 S4, 23 Sep 2025 S2. All 4 questions below, oldest first.

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Question 1
17 Jul 2023 S2
57 $A sum of money invested at a certain rate of simple interest per annum amounts to ₹14,522 in seven years and to ₹18,906 in eleven years. Find the sum invested (in ₹).$
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Question 2
19 Jul 2023 S4
75 $A sum of money at a fixed rate of simple interest amounts to ₹1,630 in 3 years and to ₹1,708 in 4 years. Find the sum (in ₹).$
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Question 3
26 Jul 2023 S4
61 $A sum of money at simple interest amounts to ₹1,200 in 3 years and to ₹1,350 in 4 years. The sum is:$
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Question 4
23 Sep 2025 S2
53 $A sum amounts to ₹6,600 in 2 years and ₹7,200 in 4 years at simple interest. What is the rate of interest per annum?$
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Question 1