Question

What same number must be added to the terms of the ratio 11:29, so that the ratio becomes 11:20?

Answer 1

Answer:

Step-by-step explanation:

find x such that

(11+x):(29+x) = 11:20

So we need to solve

20(11+x) = 11(29+x)

Equivalently,

220 + 20x = 319 + 11x

9x = 99

x = 11

Checking,

(11+11):(29+11) = 22:40 = 11:20 as required

In general:

We wish to find a general solution x = f(A,B,C,D)

such that (A+x):(B+x) = C:D.

Solution:

We need to solve the following -

D(A+x) = C(B+x)

Equivalently,

DA + Dx = CB + Cx

(D-C)x = CB - DA

x = (CB-DA)/(D-C) (as long as D does not equal C. If D=C, C:D = 1:1, and then our original ratio equation is only possible when A=B).

Note - this particular example was an example of the special case A = C; for this case, we have

f(A,B,A,D) = (AB-AD)/(D-A) = A(B-D)/(D-A) = f(A,B,D),

and in this example,

f(11,29,20) = 11(29–20)/(20–11) = 99/9 = 11.