Vijay has ₹1224 with him.
Vijay has ₹1224 with him. He divided it amongst his sons Ajay and Prakash and asked them to invest it at 4% rate of interest compounded annually. It was seen that Ajay and Prakash got same amount after 18 and 19 years respectively. How much (in ₹) did Vijay give to Prakash?
विजय के पास ₹1224 हैं। उन्होंने इसे अपने पुत्रों अजय और प्रकाश के बीच बांट दिया और उन्हें इसे वार्षिक रूप से चक्रवृद्धित 4% वार्षिक ब्याज दर पर निवेश करने को कहा। यह देखा गया कि अजय और प्रकाश को क्रमशः 18 और 19 वर्ष बाद समान धनराशि प्राप्त हुई। विजय ने प्रकाश को कितनी धनराशि (₹ में) दी थी?
Detailed Solution & Logic
600
Let amount given to Ajay = ₹x
Then amount given to Prakash = ₹(1224 − x)
Rate = 4% p.a. (compound annually)
Time:
Ajay → 18 years
Prakash → 19 years
Final amounts are equal:
$ x(1.04)^{18} = (1224 - x)(1.04)^{19} $
Divide by $(1.04)^{18}$:
$ x = (1224 - x)(1.04) $
$ x = 1272.96 - 1.04x $
$ x + 1.04x = 1272.96 $
$ 2.04x = 1272.96 $
$ x = 624 $
So, amount given to Prakash:
Answer = 1224 - 624 = 600
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