Shan has ₹1612 with him.
Shan has ₹1612 with him. He divided it amongst his sons Piyush and Manoj and asked them to invest it at 8% rate of interest compounded annually. It was seen that Piyush and Manoj got same amount after 12 and 13 years respectively. How much (in ₹) did Shan give to Piyush?
शान के पास ₹1612 हैं। उसने इसे अपने पुत्रों पीयूष और मनोज के बीच बाटं दिया तथा उन्हें इसे वार्षिक रूप से चक्रवृद्धि होने वाले 8 % ब्याज दर पर निवेश करने को कहा। यह देखा गया कि पीयूष और मनोज को क्रमशः 12 और 13 वर्ष बाद समान धनराशि प्राप्त हुई। शान ने पीयूष को कितनी धनराशि (₹ में) दी थी?
Detailed Solution & Logic
837
Let amount given to Piyush = ₹x
Then amount given to Manoj = ₹(1612 − x)
Rate = 8% p.a. (compound annually)
Time:
Piyush → 12 years
Manoj → 13 years
Final amounts are equal:
$ x(1.08)^{12} = (1612 - x)(1.08)^{13} $
Divide both sides by $(1.08)^{12}$:
$ x = (1612 - x)(1.08) $
$ x = 1740.96 - 1.08x $
$ x + 1.08x = 1740.96 $
$ 2.08x = 1740.96 $
$ x = 837 $
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