The sum of the three numbers is 123. If the ratio between the first and second is 3: 4 and that between the second and third is 3: 5, then find the second number.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 36.
( x ) is the first number,
( y) is the second number, and
( z ) is the third number.
From the ratio x / y = 3 / 4
⇒ x = 3 / 4y
From the ratio y / z = 3 / 5
⇒ z = 5 / 3
The sum of the three numbers is given as 123.
⇒ x + y + z = 123
⇒ 3 / 4y + y + 5/ 3y = 123
⇒ 3/4y = 9 / 12 , 5 / 3y = 20 / 12y
⇒9 / 12y + y + 20 / 12y = 123
⇒ 9 / 12y + 12 / 12y + 20 / 12y = 123
⇒ 41/ 12y = 123
⇒ 41y = 123 × 12
⇒ 41y = 1476
⇒ y = 1476 / 41 = 36
( x = 3 /4 × 36 = 27 )
( z = 5/3 × 36 = 60 )
⇒ x + y + z = 27 + 36 + 60 = 123
The sum is correct.
Thus, the second number is ( 36).