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

Open in App

Solution

Let the quantity be k.
Then,

$fraction numerator a plus k over denominator b plus k end fraction equals c over d$
⇒ (a + k)d = (b + k)c
⇒ ad + dk = bc + ck
⇒ ad - bc = ck - dk
⇒ ad - bc = k(c - d)
∴ k = $fraction numerator a d minus b c over denominator c minus d end fraction equals k$

Suggest Corrections

Similar questions

What must be added to each term of the ratio 2 : 3, so that it may become equal to 4:5?

What quantity must be added to each term of the ratio $6 : 11$ so that it becomes equal to $2 : 3$ ?

What quantity must be added to each term of the ratio 7:13 so as to make it equal to 9:11

a^{2} : b^{2}

a : b

Join BYJU'S Learning Program