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
Find the number which bears the same ratio to `7/33` that `8/21` does to `4/9`.
Convert the following percentage to fractions and ratio:
25%
Express the following ratios in its simplest form :
`2 1/3 : 3 1/2: 1 1/4`
Find the mean proportional between 0.6 and 9.6
Which ratio is greater:
`3/7` or `6/13`
A 35-cm line segment is divided into two parts in the ratio 4 : 3. Find the length of each part.
Fill in the place holder:
Find the simplified form of the following ratio.
12 : 27
In the following figure, division represents 1 cm:
Express numerically the ratios of the following distances:
BF : AI
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?
