What number must be added to each of the numbers 15, 9 and 5 so that the resulting numbers may be in a continued proportion ?
3
Given:
15, 9, 5 are in continuous ratio
Used Concept:
If a, b, and c are in continuous ratio, then,
⇒ a/b = b/c
⇒ b2 = a × c
We can also say that b is the harmonic mean of a and c
.
Calculation:
Let x be added to each of 15, 9, and 5, then the resulting numbers will be
⇒ (15 + x), (9 + x), (5 + x)
If these numbers are in continuous ratio, then,
⇒ (9 + x)2 = (15 + x)(5 + x)
⇒ 81 + x2 + 18x = 75 + 20x + x2
⇒ 20x - 18x = 81 - 75
⇒ 2x = 6
⇒ x = 3
∴ To have the resulting numbers in continuous ratio, each number 15, 9, and 5 should have 3 added to it.
Important Questions from Mean Proportional
When x is subtracted from each of 43, 38, 11 and 10, then the numbers so obtained in this order are in proportion. What is the mean proportional between (11x + 3) and (9x - 2) ?
Find the mean proportional between 4 and 900.
If 22, x, 88 are in a continued proportion, find the value of x.
A. 24
B. 33
C. 44
D. 36
The arithmetic mean and geometric mean of two numbers are 7 and 2√10 respectively, then find the numbers.
When x is subtracted from each of 24, 30, 36 and 46, the numbers so obtained in this order, are in proportion. What is the mean proportional between (2x + 3) and (3x + 2)?
