Question

The sum of three no. is 285.Ratio between second and third no. is 6:5.Ratio between first and second no. is 3:7.The third no. is?

Answer 1

$\underline \bold{GIVEN}$

◼Sum of three numbers = $\mathsf{285}$

◼Ratio between second and third =$\mathsf{ 6:5}$

◼Ratio between first and second= $\mathsf{ 3:7}$

✳Let the these three numbers be $\mathsf{a,b \: and \: c}$

So the ratios are,

$\bigstar \mathsf{b:c = 6:5}$-(1)

$\bigstar \mathsf{a:b = 3:7}$-(2)

✳At first we need to make these three numbers in continued proportion and for that we need to make b same for both ratios.

So,

Multiply eq (1) by 7 and eq(2) by 6.

$\bigstar \mathsf{b:c = 6:5}$-(1) × 6

$\bigstar \mathsf{a:b = 3:7}$-(2) ×7

So, ratio becomes

$\bigstar \mathsf{b:c = 42:35}$

$\bigstar \mathsf{a:b = 18:42}$

Now the are in continued proportion

$\mathsf{a:b:c = 18 : 42 : 35}$

✳Let the common ratio be x, so number becomes

$\mathsf{ 18x ,42 x \:and \:35x}$

Since the sum of these three is 258 so,

$\mathsf{ 18x + 42 x + 35x= 285}$

$\mathsf{ 95x = 285}$

$\mathsf{x = \dfrac{285}{95}}$

$\large \boxed{x =3}$

So, the numbers will be,

$\boxed{\mathsf{ 18 \times 3 = 54}}$

$\boxed{\mathsf{ 42 \times 3 = 126}}$

$\boxed{\mathsf{ 35 \times 3 = 105}}$