Question

The two numbers are in the ratio of 1/3 . If 10 is subtracted from each term of the ratio, th ratio becomes 5/12 . Find the numbers.​

Answer 1

Let the two numbers be x and 3x.

• Subtract 10 from each of these numbers. We get x-10 and 3x-10. From the given problem, the ratio of these new numbers is 5:12. Then,

$\Longrightarrow \sf \: \dfrac{x - 10}{3x - 10} = \dfrac{5}{12}$

Cross Multiplying

$\Longrightarrow \sf \: 12(x - 10) = 5(3x - 10)$

$\Longrightarrow \sf \: 12x - 120 = 15x - 50$

$\Longrightarrow \sf \: 12x - 15x = 120 - 50$

$\Longrightarrow \sf \: - 3x = 70$

$\Longrightarrow \sf{ \boxed{ \: x = \frac{ - 70}{3} }}$

The required numbers are

• $\sf{x= \dfrac{-70}{3}}$ and

• $\sf{3x= \dfrac{-70×3}{3}=\bf -70}$

Answer 2

Step-by-step explanation:

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