Question
Download Solution PDFA lent a part of Rs.26200 to X at 10% simple interest. Rest to Y at 5% at simple interest. After 4 years he got an amount of Rs.34060 in total. Then what is the amount lent to Y? (In Rs.)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Total amount lent = Rs.26200
Interest rate for X = 10% per annum
Interest rate for Y = 5% per annum
Total time = 4 years
Total amount after 4 years = Rs.34060
Formula Used:
Simple Interest (SI) = (Principal × Rate × Time) / 100
Total amount = Principal + Simple Interest
Calculation:
Let the amount lent to X = Rs.x
Amount lent to Y = Rs.(26200 - x)
Interest from X = (x × 10 × 4) / 100 = (40x) / 100 = 0.4x
Interest from Y = [(26200 - x) × 5 × 4] / 100 = [(26200 - x) × 20] / 100 = (524000 - 20x) / 100 = 5240 - 0.2x
Total amount after 4 years = Principal + Interest
⇒ 26200 + (0.4x + 5240 - 0.2x) = 34060
⇒ 26200 + 5240 + 0.2x = 34060
⇒ 31440 + 0.2x = 34060
⇒ 0.2x = 34060 - 31440
⇒ 0.2x = 2620
⇒ x = 2620 / 0.2
⇒ x = 13100
Amount lent to Y = 26200 - x
⇒ Amount lent to Y = 26200 - 13100
⇒ Amount lent to Y = 13100
The amount lent to Y is Rs.13100.
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