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.
संबंधित प्रश्न
If `(28 - x)` is the mean proportional of `(23 - x)`and `(19 - x)` then find the value of x.
Find the value of the unknown in the following proportion :
c
If a, b, c and dare in continued proportion, then prove that
(a+ d)(b+ c)-(a+ c)(b+ d)= (b-c)2
If `a/b = c/d = r/f`, prove that `((a^2b^2 + c^2d^2 + e^2f^2)/(ab^3 + cd^3 + ef^3))^(3/2) = sqrt((ace)/(bdf)`
Find the third proportional to 5, 10
Find the third proportional to Rs. 3, Rs. 12
Determine if the following ratio form a proportion:
200 mL : 2.5 L and Rs 4 : Rs 50
If q is the mean proportional between p and r, prove that: p3 – 3q2 + r2 = `q^4(1/p^2 - 3/q^2 + 1/r^2)`
Are the following statements true?
7.5 litres : 15 litres = 5 kg : 10 kg
The mean proportion between `3 + 2sqrt(2)` and `3 - 2sqrt(2)` is ______.
