Advertisements
Advertisements
प्रश्न
What least number must be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion?
What number must be subtracted from each of number 7, 17, 47 so that the remainder may be in continued proportion?
Advertisements
उत्तर
Let the number subtracted be x.
∴ (7 – x) : (17 – x) :: (17 – x)(47 – x)
⇒ `(7 - x)/(17 - x) = (17 - x)/(47 - x)`
⇒ (7 – x) (47 – x) = (17 – x) (17 – x)
Left side:
7 × 47 − 7x − 47x + x2 = 329 − 54x + x2
Right side:
(17−x)2 = 289 − 34x + x2
⇒ 329 − 54x + x2 = 289 − 34x + x2
⇒ 329 − 54x = 289 − 34x
⇒ 329 – 289 = 54x − 34x
⇒ 40 = 20x
⇒ x = `20/40`
⇒ x = 2
Thus, the required number which should be subtracted is 2.
APPEARS IN
संबंधित प्रश्न
If a/b = c/d prove that each of the given ratio is equal to `(13a - 8c)/(13b - 8d)`
Using properties of proportion, solve for x:
`(sqrt(x + 1) + sqrt(x - 1))/(sqrt(x + 1) - sqrt(x - 1)) = (4x - 1)/2`
If x and y be unequal and x : y is the duplicate ratio of x + z and y + z, prove that z is mean proportional between x and y.
Find the value of the unknown in the following proportion :
`1/2 : "m" :: 14/9 : 4/3`
Find the smallest number that must be subtracted from each of the numbers 20, 29, 84 and 129 so that they are in proportion.
If a, b, c and dare in continued proportion, then prove that
`sqrt (("a + b + c")("b + c + d")) = sqrt "ab" + sqrt "bc" + sqrt "cd"`
Using the properties of proportion, solve for x, given. `(x^4 + 1)/(2x^2) = (17)/(8)`.
If a, b, c, d are in continued proportion, prove that:
`sqrt(ab) - sqrt(bc) + sqrt(cd) = sqrt((a - b + c) (b - c + d)`
Find two numbers such that the mean proportional between them is 28 and the third proportional to them is 224.
If b is the mean proportional between a and c, prove that (ab + bc) is the mean proportional between (a² + b²) and (b² + c²).
