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 :

Options

A. 1:2
B. 5:3
C. 2:3
D. 4:5

Answer

To solve the problem, we need to analyze the given ratios and find the ratio of Sukhoi to MiG. Let's denote:

- Sukhoi = S
- MiG = M
- Jaguar = J

### Step 1: Set up the equations based on the ratios

From the first statement, we have:
1. The ratio of Sukhoi to MiG and Jaguar together is 5:7.
\[ \frac{S}{M + J} = \frac{5}{7} \]
This can be rewritten as:
\[ 7S = 5(M + J) \quad \text{(Equation 1)} \]

From the second statement, we have:
2. The ratio of Jaguar to Sukhoi and MiG together 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

From Equation 2, we can express J:
\[ J = \frac{S + M}{2} \]

### Step 3: Substitute J into Equation 1

Now, substitute J in Equation 1:
\[ 7S = 5(M + \frac{S + M}{2}) \]
Expanding this gives:
\[ 7S = 5(M + \frac{S}{2} + \frac{M}{2}) = 5(\frac{3M}{2} + \frac{S}{2}) \]
This simplifies to:
\[ 7S = \frac{15M + 5S}{2} \]
Multiplying through by 2 to eliminate the fraction:
\[ 14S = 15M + 5S \]
Rearranging gives:
\[ 14S - 5S = 15M \]
\[ 9S = 15M \]
Dividing both sides by 3:
\[ 3S = 5M \]

### Step 4: Find the ratio of Sukhoi to MiG

Now we can express the ratio of Sukhoi to MiG:
\[ \frac{S}{M} = \frac{5}{3} \]

### Final Answer

Thus, the ratio of Sukhoi to MiG is:
\[ \text{Sukhoi : MiG} = 5 : 3 \]

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