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.

$13x+16x+24x=212$

$53x=212$

$x=\dfrac{212}{53}$

$x=4$

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.