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Question

In what time will $2500 lent at 2% per annum on simple interest earn as much interest as $3000 will earn in 5 years at 5% per annum on simple interest?

A
25 years
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B
5 years
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C
10 years
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D
15 years
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Solution

The correct option is D 15 years
Given, P1 = Principal=$2500
R1 = Rate of interest=2%
Let time period be T1
Simple Interest1=PRT100=2500×2×T1100

and P2 = Principal=$3000
R2 = Rate of interest=5%
T2 = Time period = 5 years
Simple Interest2=PRT100=3000×5×5100

According to question,
Simple Interest1=Simple Interest2
2500×2×T1100=3000×5×5100
25×100×2×T1100=30×100×5×5100

Cancel out common factors, we get
25×2×T1=30×5×5
50×T1=150×5
50×T1=750

Dividing both the sides by 50, we get
T1=75050

Simplify and cancel out common factors, we get

T1=15×5050
T1=15

Hence, required time period is 15 years.

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