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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.
