The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is:
49
48
30
20
Solution
Let the numbers be x, y and z.
Then,
x : y = 2 : 3
y : z = 5 : 8
$\therefore$ x : y : z = 2 × 5 : 3 × 5 : 3 × 8
= 10 : 15 : 24
Sum of the rations
= 10 + 15 + 24 = 49
$\therefore$ The second number
$= \dfrac {15}{49} \times 98 = 30$