Mahesh has ₹1617 with him.
Mahesh has ₹1617 with him. He divided it amongst his sons Vijay and Ajay and asked them to invest it at 10% rate of interest compounded annually. It was seen that Vijay and Ajay got same amount after 15 and 16 years respectively. How much (in₹) did Mahesh give to Vijay?
महेश के पास ₹1617 हैं। उसने इसे अपने पुत्रों विजय और अजय के बीच बांट दिया तथा उन्हें इसे वार्षिक रूप से चक्रवृद्धि होने वाली 10% ब्याज दर पर निवेश करने को कहा। यह देखा गया कि विजय और अजय को क्रमश: 15 और 16 वर्ष बाद समान धनराशि प्राप्त हुई। महेश ने विजय को कितनी धनराशि (₹ में) दी थी?
Detailed Solution & Logic
Correct Answer:
847
Let amount given to Vijay = $ x $
Then amount given to Ajay = $ 1617 - x $
Rate = 10% p.a. (compound annually)
Time: Vijay → 15 years, Ajay → 16 years}
Final amounts are equal:
$ x (1.1)^{15} = (1617 - x)(1.1)^{16} $
Divide both sides by (1.1)^{15}: $
$ x = (1617 - x) \cdot 1.1 $
$ x = 1778.7 - 1.1x $
$ x + 1.1x = 1778.7 $
$ 2.1x = 1778.7 $
$ x = \frac{1778.7}{2.1} = 847 $
Answer = ₹847
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