Question

The sum of 3 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 :​

Answer 1

Step-by-step explanation:

Given:-

The sum of 3 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.

To find :-

Find the second number?

Solution :-

Let the three numbers be X , Y and Z

The ratio of the first and the second numbers = 2:3

=> X:Y = 2:3

=> X/Y = 2/3

=> X/Y = (2/3)×(5/5)

=> X/Y = (2×5)/(3×5)

=> X/Y = 10/15

=> X:Y = 10:15 --------------(1)

Let X = 10 a and Y = 15 a

The ratio of the second and the third numbers = 5:8

=> Y : Z = 5:8

=> Y/Z = 5/8

=> Y/Z = (5/8)×(3/3)

=> Y/Z = (5×3)/(8×3)

=> Y/Z = 15/24

=> Y: Z = 15:24 -------------(2)

Let Y = 15

Now,

X : Y = 10 : 15

Y : Z = 15 : 24

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X : Y : Z = 10 : 15 : 24

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Let X = 10a , Y = 15a and Z = 24a

Sum of the three numbers = 98

=> X+Y +Z = 98

=> 10a+15a+24a = 98

=> 49a = 98

=> a = 98/49

=> a = 2

First number = 10a = 10×2 = 20

X = 20

and

second number = Y = 15a

=> Y = 15×2

=> Y = 30

and Third Number = 24a

=> 24×2

=> Z = 48

Therefore, X = 20 , Y = 30 and Z = 48

Answer:-

The second number for the given problem is 30

Used formulae:-

• a : b can be written as a/b