Two numbers are in the ratio 10:4 and when 3 is added to both the numbers ratio becomes 3:1. Find the numbers.

-30 and -12

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27 and 9

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-20 and -8

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30 and 12

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Solution

The correct option is A
-30 and -12

Let the numbers be 10 $x$ and 4 $x$ .

When 3 is added to both numbers the new numbers will be 10x + 3 and 4x + 3.

Now, $\frac{10 x + 3}{4 x + 3} = \frac{3}{1}$

$\Rightarrow (10 x + 3) \times 1 = (4 x + 3) \times 3$

$= 10 x + 3 = 12 x + 9$

$= - 2 x = 6$

$= x = - 3$

So, the numbers are

$10 x = 10 \times - 3 = - 30$ and

$4 x = 4 \times - 3 = - 12$

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Two numbers are in the ratio 10:4 and when 3 is added to both the numbers ratio becomes 3:1. Find the numbers.

The correct option is A -30 and -12 Let the numbers be 10x and 4x. When 3 is added to both numbers the new numbers will be 10x + 3 and 4x + 3. Now, 10x+34x+3=31 ⇒(10x+3)×1=(4x+3)×3 =10x+3=12x+9 =−2x=6 =x=−3 So, the numbers are 10x=10×−3=−30 and 4x=4×−3=−12