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 Sukhol and mig:

Options

A. `2:7`
B. `3:5`
C. `3:1`
D. `5:3`

Answer

To solve the problem step by step, we need to find the ratio of Sukhoi (S) to MIG (M) given the two ratios involving Jaguar (J).

### Step 1: Set up the equations based on the given ratios.
From the problem, we have two ratios:
1. The ratio of Sukhoi to the sum of MIG and Jaguar is 5:7.
\[ \frac{S}{M + J} = \frac{5}{7} \]
This can be rewritten as:
\[ 7S = 5(M + J) \quad \text{(Equation 1)} \]

2. The ratio of Jaguar to the sum of Sukhoi and MIG is 1:2.
\[ \frac{J}{S + M} = \frac{1}{2} \]
This can be rewritten as:
\[ 2J = S + M \quad \text{(Equation 2)} \]

### Step 2: Express J in terms of S and M using Equation 2.
From Equation 2, we can express J as:
\[ J = \frac{S + M}{2} \]

### Step 3: Substitute J in Equation 1.
Now substitute the expression for J into Equation 1:
\[ 7S = 5\left(M + \frac{S + M}{2}\right) \]
Simplifying the right side:
\[ 7S = 5\left(M + \frac{S}{2} + \frac{M}{2}\right) \]
\[ 7S = 5\left(\frac{2M + S}{2}\right) \]
\[ 7S = \frac{5(2M + S)}{2} \]
Multiplying both sides by 2 to eliminate the fraction:
\[ 14S = 5(2M + S) \]
Expanding the right side:
\[ 14S = 10M + 5S \]

### Step 4: Rearranging the equation.
Now, rearranging the equation to isolate S and M:
\[ 14S - 5S = 10M \]
\[ 9S = 10M \]

### Step 5: Find the ratio of S to M.
Dividing both sides by M and S:
\[ \frac{S}{M} = \frac{10}{9} \]
Thus, the ratio of Sukhoi to MIG is:
\[ S:M = 10:9 \]

### Step 6: Final Ratio of Sukhoi and MIG.
To express the ratio in a more standard form:
\[ S:M = 10:9 \]