A sum of money was divided between Cyrus, Rohan and Mishti. The ratio of the sums received by Cyrus and Rohan

Question

A sum of money was divided between Cyrus, Rohan and Mishti. The ratio of the sums received by Cyrus and Rohan was 3 : 2 , while the ratio of the sums received by Rohan and Mishti was 7 : 12 . If the sum received by Cyrus was ₹1,800 less than the sum received by Mishti, how many rupees did Rohan rece

Accepted Answer

Let the shares of Cyrus, Rohan, and Mishti be

C

,

R

, and

M

respectively.Given:

C : R = 3 : 2

R : M = 7 : 12

To find a combined ratio

C : R : M

, we equalize the value of

R

:Multiply

C : R

by 7:

C : R = 21 : 14

Multiply

R : M b y 2 :

R : M = 14 : 24

S o, t h eco mbin e d r a t i o i s

C : R : M = 21 : 14 : 24

. L e tt h es ha res b e

21k

,

14k

, an d

24k

. G i v e n t ha tC yr u srece i v e d ₹1, 800 l ess t han M i s h t i :

M - C = 1800

$

24 k - 21 k = 1800

3 k = 1800 ⟹ k = 600

Rohan's share (

R

) =

14 k = 14 \times 600 = ₹8, 400

.

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