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## Explanation

- The sum of three numbers is 136.
- If the ratio between first and second be 2:3.
- And between second and third is 5:3.
- The second number can be find out in this way.

Let suppose three numbers are a, b and c.

The sum of a, b and c is 136.

a + b + c = 136 ________ (i)

Ratio between first and second is 2 : 3.

a : b = 2 : 3 ________ (ii)

Ratio between second and third is 5 : 3.

b : c = 5 : 3 ________ (iii)

By solving these three equations [equation (i), (ii) and (iii)] simultaneously, we can easily figure out the second number (b = 60).

## To Find

Second Number = ?

## Solution

Let suppose three numbers are a, b and c.

According to the first given condition (the sum of three numbers is 136).

a + b + c = 136

Multiplying both sides with 5

5a + 5b + 5c = 680 ________ (A)

According to second given condition

a/b = 2/3

3a = 2b

3a – 2b = 0

Multiplying both sides of equation with 3

9a – 6b = 0 ________ (ii)

and

b/c = 5/3

3b = 5c

3b – 5c = 0 ________ (iii)

Adding equation (ii) and (iii)

3a + b – 5c = 0 ________ (B)

Adding equation (A) and (B)

5a + 3a + 5b + b + 5c – 5c = 680 + 0

8a + 6b = 680 ________ (iv)

Adding equation (ii) and (iv)

8a + 9a + 6b – 6b = 680 + 0

17a = 680

a = 680/17

a = 40

Put a = 40 in equation (ii)

9(40) – 6b = 0

360 – 6b = 0

6b = 360

b = 60

**Second Number = 60 answer**

## Conclusion

The sum of three numbers is 136. If the ratio between first and second be 2:3 and that between second and third is 5:3, then the second number is 60.