Question

the sum of three numbers is 92 if the ratio of first and second number is 3:4 and the ratio of first and third number is 2 : 4 find the second number​

Answer 1

GIVEN,

Sum of two numbers is$\mathsf{92}$

Let the three variables be a,b and c.

Ratio of first to second =$\mathsf{3:4}$

so,

$\mathsf{a:b=3:4}$-----(1)

Ratio of first to third = $\mathsf{3:4}$

so,

$\mathsf{a:c=2:4}$-----(2)

$\dfrac{a}{b} =\dfrac{3}{4} \\\\\dfrac{a}{c} =\dfrac{2}{4}$

We will make it  in continued proportion for that we had to make a same for both ratio.

So, multiply (1) by 2 and (2) by 3

$\mathsf{a:b=3:4}$ *2

$\mathsf{b a:b=6 : 8}$

$\mathsf{a:c=2:4}$ *3

$\mathsf{b a:c=6 : 12}$

So,

$\mathsf{a:b:c=6:8:12}$

Now , let the common ratio be $\mathsf{x}$

The ratio becomes,

6x , 8x and 12x.

According to question

$\mathsf{6x +8x + 12x = 92}$

$\mathsf{26x= 92}$

$\mathsf{x=\dfrac{92}{26}}$

$\mathsf{x=3.53}$

So , the numbers are

$\mathsf{First\: number \implies 6 \times 3.53 = 21.18}$

$\mathsf{Second \: number \implies 8 \times 3.53 = 28.24}$

$\mathsf{Third \: number \implies 12 \times 3.53 = 42.36}$