Question

What quantity must be added to each term of the ratio x:y so that it may become equal to c:d?

Answer 1

Let 'm' be subtracted from both terms of the given ratio.

∴ By the problem,

(x+m)/(y+m)=c/d
⇒dx+dm=cy+cm
⇒(d-c)m=cy-dx
⇒m=(cy-dx)/(d-c)

Hence,the required term to be added is : (cy-dx)/(d-c). (Ans.)

Answer 2

Adding a quantity to both Numerator and Denominator

Step-by-step explanation:

Let the required quantity which is to be added be p.  

Then, we have:

$\frac {x+p}{y+p} = \frac {c}{d}$

⇒ dx+pd=cy+cp

⇒ pd - cp = cy - dx

⇒ p(d-c) = cy-dx

⇒ p = $\frac {cy-dx}{d-c}$