Question

If the difference between compound interest (interest compounded yearly) and simple interest on a certain sum at the rate 20% p.A. After 3 years is rs.1280 then what is the principal? (a) 7,900 (b) 8,000 (c) 10,000 (d) 8,300

Answer 1

$<b>Heya mate. (^_-). Solution below.$
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• Given Rate of interest (R) = 20% p.a.

• Given Time (T) = 3 years


• Let the Principal be 'x'.



• Then, simple interest (S.I) -

= P × R × T/100

= x × 20 × 3/100

= 60x/100

= 3x/5



• And, Compound interest (C.I) -

= A - P

= [ P × {1 + (R/100)}^t ] - P

= [ x × {1 + (20/100)}³ ] - x

= [ x × {(100 + 20/100)}³ ] - x

= [ x × (120/100)³ ] - x

= [ x × (6/5)³ ] - x

= [ x × 216/125 ] - x

= 216x/125 - x

= (216x - 125x)/125

= 91x/125



• Now, according to the question, the difference between C.I and S.I is Rs. 1280.


=> 91x/125 - 3x/5 = 1280

=> (91x - 75x)/125 = 1280

=> 16x/125 = 1280

=> x = 1280 × 125/16

=> x = 160000/16

=> x = 10000

• Therefore, the Principal = x = 10000 Rs.

$<marquee>Hence, your answer is 10000 Rs (option C).</marquee>$
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Thank you.. ;-)