Advertisements
Advertisements
Question
What least number must be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion?
Solution
Let the number subtracted be x.
∴ (7 – x) : (17 – x) :: (17 – x)(47 – x)
`(7 - x)/(17 - x) = (17 - x)/(47 - x)`
(7 – x)(46 – x) = (17 – x)2
329 – 47x – 7x + x2 = 289 – 34x + x2
329 – 289 = –34x + 54x
20x = 40
x = 2
Thus, the required number which should be subtracted is 2.
APPEARS IN
RELATED QUESTIONS
Find the third proportional to a – b and a2 – b2
Find the third proportional to `x/y + y/x` and `sqrt(x^2 + y^2)`
If a, b and c are in continued proportion, prove that: a: c = (a2 + b2) : (b2 + c2)
Find the third proportion to the following :
3 and 15
Find the third proportion to the following :
(x - y) and m (x - y)
Find the third proportional to:
`a/b + b/c, sqrt(a^2 + b^2)`.
If a + c = mb and `(1)/b + (1)/d = m/c`, prove that a, b, c and d are in proportion.
If a, b, c are in continued proportion, prove that: a2 b2 c2 (a-4 + b-4 + c-4) = b-2(a4 + b4 + c4)
Choose the correct answer from the given options :
If x, 12, 8 and 32 are in proportion, then the value of x is
If b : a = c : d, then a, b, c, d are in proportion.
