Question : The sum of the three numbers is 280. If the ratio between the first and second numbers is 2 : 3 and the ratio between the second and third numbers is 4 : 5, then find the second number.
Option 1: 80
Option 2: 90
Option 3: 86
Option 4: 96
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Correct Answer: 96
Solution :
Given: The sum of the three numbers is 280.
The ratio between the first and second numbers is 2 : 3 and the ratio between the second and third numbers is 4 : 5.
Let the three numbers be P, Q, and R.
According to the question,
P + Q + R = 280
P: Q = 2 : 3
Q: R = 4 : 5
Make the ratio equal by multiplying the first ratio with 4 and the second ratio with 3.
⇒ P : Q : R = 8 : 12 : 15
According to the question,
$8x+12x+15=280$
⇒ $35x=280$
⇒ $x=8$
The second number Q = $12x=12\times 8=96$.
Hence, the correct answer is 96.
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