Advertisements
Advertisements
प्रश्न
If (a – x) : (b – x) be the duplicate ratio of a: b show that:
`(1)/x = (1)/a + (1)/b.`
Advertisements
उत्तर
Here (a - x) : (b - x) is duplicate ratio of a : b
∴ `a^2/b^2 = (a - x)/(b - x)`
⇒ `a^2b - a^2x = b^2a - b^2x`
⇒ `a^2b - b^2a = a^2x - b^2x`
⇒ ab (a - b) = x (a - b) (a + b)
⇒ ab = x (a + b)
⇒ `(1)/x = (a + b)/(ab)`
⇒ `(1)/x = (1)/a + (1)/b`
Hence proved.
संबंधित प्रश्न
If `(m + n)/(m + 3n) = 2/3`, find : `(2n^2)/(3m^2 + mn)`.
In a basket, the ratio between the number of oranges and the number of apples is 7 : 13. If 8 oranges and 11 apples are eaten, the ratio between the number of oranges and the number of apples becomes 1 : 2. Find the original number of oranges and the original number of apples in the basket.
Find the duplicate ratio of `2sqrt(2) : 3sqrt(5)`
Find the compounded ratio of the following:
(m-n):(m+n), (m+n)2 : (m2+n2) and (m4 - n4): (m2-n2) 2
Find: The duplicate ratio of 7: 9
If 4, x and 9 are in continued proportion, find the value of x.
30 cricket players and 20 kho-kho players are training on a field. What is the ratio of cricket players to the total number of players?
If the cost of 30 packets of 8 pencils each is Rs 600, what is the cost of 25 packets of 12 pencils each?
If `x/a = y/b = z/c`, prove that `(3x^3 - 5y^3 + 4z^3)/(3a^3 - 5b^3 + 4c^3) = ((3x - 5y + 4z)/(3a - 5b + 4c))^3`.
A carpenter had a board which measured 3 m × 2 m. She cut out a rectangular piece of 250 cm × 90 cm. What is the ratio of the area of cut out piece and the remaining piece?
