In the Squadron of Indian Air Force the ratio of Sukhoi is to Mig and Jaguar together is 5:7

Ques - In the Squadron of Indian Air Force the ratio of Sukhoi is to Mig and Jaguar together is 5:7 and the ratio of Jaguar is to Sukhoi and Mig together is 1: 2. Find the ratio of Sukhoi and Mig:

(a) 2 : 7

(b) 3 : 5

(c) 3 : 1

(d) 5 : 3

Solution - 

Let,

Sukhoi = S

Mig = M

Jaguar = J

then,

The ratio of Sukhoi is to Mig and Jaguar together is 5:7.

S / ( M + J ) = 5 / 7

7S = 5 (M + J )

7S = 5M + 5J ----(1)

And,

The ratio of Jaguar is to Sukhoi and Mig together is 1: 2.

J / (S + M ) = 1 / 2

2J = S + M -----(2)

As we need ,

The ratio of Sukhoi and Mig (S : M)

so,

By substituting eq. 2 in eq. 1 we get,

7S = 5M + 5J ----(1)

2J = S + M

J = (S + M) / 2 -----(2)

7S = 5M + 5 [(S+M) / 2]

14S = 10M + 5S + 5M

14S - 5S = 10M + 5M

9S = 15M

Therefore,

S / M = 15 / 9

S : M = 5 : 3

Thus,

The ratio of Sukhoi and Mig = 5 : 3.

Hence,

The correct answer is option (d) 5 : 3.

Thank You