Question

Three numbers X, Y, and Z are in the ratio 2:7:8. If 12 is subtracted from Y, then three numbers form a geometric sequence (in the order X, Y–12, Z). Find X, Y, and Z.

Answer 1

Explanation:

x:y:z = 2:7:8 => x = 2/7 y ; z = 7/8y (1)

According to the mean of geometric sequence, we could get :

(y-12) = x.z (2)

based on (1) and (2)

we could get y1 = 28, y2 = 84/11 (3)

based on (3) and (1)

we could get x1 = 8, z1 = 32 ; x2 = 24/11, z2 = 96/11