Question

What number must be subtracted from each of
the numbers 12, 18, 28 so that the remainders
may be in continued proportion?​

Answer 1

Question :

What number must be subtracted from each of the numbers 12, 18, 28 so that the remainders may be in continued proportion?

Hint :

One should be subtracted from 4, 10 and 28 so that the remaining numbers 3, 9 and 27 are in a continued for proportion

Solution :

Let the number be x, such that

(4-x):(10-x)=(10-x):(28-x), or

(10-x)^2 = (4-x)(28-x), or

100 - 20x + x^2 = 112– 32x + x^2, or

32x-20x = 112–100, or

12x = 12, or

x = 12/12

x = 1.

So let check it

(4-x):(10-x)=(10-x):(28-x), or

(4–1):(10–1)=(10–1):(28–1), or

3:9 = 9:27, or

3*27 = 9^2, or

LHS = 81

RHS = 81

Hence our answer is right !