Question
Download Solution PDFA person invested an amount of X at the rate of 18% simple interest per annum and an amount of Y at the rate of 12% simple interest per annum. He received an interest of ₹4,320/- at the end of the year. Had he interchanged the amounts invested, he would have received an interest of ₹4,680/-. Then |X-Y| =
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Total interest recieved on Rs x at 18% and Rs y at 12% = ₹4,320
Interest if interchanged = ₹4,680
Formula used:
Simple Interest (SI) = (Principal × Rate × Time) / 100
|X - Y| = Difference in Principal amounts
Calculation:
Let X and Y be the amounts invested:
From the first condition: SI = (X × 18 × 1)/100 + (Y × 12 × 1)/100 = 4,320
⇒ (18X + 12Y)/100 = 4,320
⇒ 18X + 12Y = 4,32,000 (Equation 1)
From the second condition (interchanged): SI = (X × 12 × 1)/100 + (Y × 18 × 1)/100 = 4,680
⇒ (12X + 18Y)/100 = 4,680
⇒ 12X + 18Y = 4,68,000 (Equation 2)
Subtract Equation 1 from Equation 2:
⇒ (12X + 18Y) - (18X + 12Y) = 4,68,000 - 4,32,000
⇒ -6X + 6Y = 36,000
⇒ -X + Y = 6,000 ⇒ X - Y = -6,000
∴ |X - Y| = ₹6,000
The correct answer is option (4).
Last updated on Sep 27, 2023
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