Question

The sum of three numbers is 212 .If the ratio of the first to the second is 13:16 and that of the second to the third is 2:3 then find the numbers.`​

Answer 1

Given:

The sum of three numbers is 212 .

The ratio of the first to the second is 13:16 and that of the second to the third is 2:3.

To find:

The unknown numbers.

Solution:

We have,

First : Second = 13:16

Second: Third = 2:3

We need to combine these ratios, to get a single ratio for all three numbers.

Second: Third = 2×8:3×8 = 16:24

Now,

First: Second: Third = 13:16:24

Let the first, second and third numbers are 13x, 16x and 24x respectively.

`13x+16x+24x=212`

`53x=212`

`x=(212)/(53)`

`x=4`

So, the numbers are,

`First=13x`

`First=13(4)`

`First=52`

Similarly,

`Second=16x`

`Second=16(4)`

`Second=64`

And,

`Third=24x`

`Third=24(4)`

`Third=96`

Therefore, the three unknown numbers are 52, 64, 96.