Question

If 2 is subtracted from a ratio, it becomes 1:2. Find the ratio.​

Answer 1

Answer:

Let the required numbers be x and y.

Now, we have:  x+2/ y+2 = 1/2  

By cross multiplication,

we get:  2x + 4 = y + 2  ⇒ 2x – y = -2 ……(i)  

Again, we have:  x−4/ y−4 = 5/11  

By cross multiplication,

we get:  11x – 44 = 5y – 20  ⇒11x – 5y = 24 ……(ii)  

On multiplying (i) by 5, we get:  10x – 5y = -10  

On subtracting (iii) from (ii), we get:  x = (24 + 10) = 34  

On substituting x = 34 in (i),

we get:  2 × 34 – y = -2  ⇒ 68 – y = -2  ⇒ y = (68 + 2) = 70

Hence, the required numbers are 34 and 70.

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Answer 2

Answer:

Original ratio is $5 : 2$ .

Step-by-step explanation:

To find : original ratio.

Given : when 2 is subtracted from a ratio, it becomes 1:2.

Solution :

• As per given data we know that , when 2 is subtracted from a ratio, it becomes 1 : 2 .
• Let , $x : y$  be the original ratio .
• According to given condition we write as , $\frac{x}{y} -2 = \frac{1}{2}$
• To find ratio we transpose constants at RHS , leaving variables at LHS .

        $\frac{x}{y} -2 = \frac{1}{2} \\\\\frac{x}{y} = \frac{1}{2}+ 2 \\\\\frac{x}{y} = \frac{1 + 4 }{2} \\\\\frac{x}{y} = \frac{5}{2}$