Question

Five children each owned a different number of rupees. The ratio of any one’s fortune to
the fortune of every child poorer than himself was an integer. The combined fortune of
the children was 847 rupees. The least number of rupees that a child had was
(A) 12 Rs. (B) 10 Rs. (C) 7 Rs. (D) 5 Rs.

Answer 1

Given:  Five children each owned a different number of rupees. The ratio of any one’s fortune to  the fortune of every child poorer than himself was an integer. The combined fortune of  the children was 847 rupees.

To Find : The least number of rupees that a child had was

(A) 12 Rs. (B) 10 Rs. (C) 7 Rs. (D) 5 Rs.

Solution:

Let say  least number of rupees that a child had = K

Then other child has

KA , KB , KC , KD  where A , B , C , & D are integers

Total amount

= K + KA + KB + KC + KD

= K ( 1 + A + B + C + D)

847  = 7 x 11 x 11

K = 7  

. The least number of rupees that a child had was Rs  7

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