Advertisements
Advertisements
प्रश्न
If a: b with a ≠ b is the duplicate ratio of a + c: b + c, show that c2 = ab.
Advertisements
उत्तर
The duplicate ratio of
`a/b = ((a + c)^2)/((b + c)^2)`
⇒ `a/b = (a^2 + c^2 + 2ac)/(b^2 + c^2 + 2bc)`
⇒ ab2 + ac2 + 2abc = a2b + bc2 + 2abc
⇒ ac2 - bc2 = a2b - ab2
⇒ c2(a - b) = ab(a - b)
Hence, c2 = ab.
Hence proved.
संबंधित प्रश्न
Convert the following ratio to a percentage.
3 : 4
The work done by (x – 2) men in (4x + 1) days and the work done by (4x + 1) men in (2x – 3) days are in the ratio 3 : 8. Find the value of x.
If (p – x) : (q – x) be the duplicate ratio of p : q then show that : `1/p + 1/q = 1/x`.
What quantity must be added to each term of the ratio (p + q) : (p - q) to make it equal to (p + q)2 : (p - q)2 ?
The population of the town is 180,000, out of which males are `1/3` of the whole population. Find the number of females. Also, find the ratio of the number of females to the whole population.
If P : Q = `1/2 : 1/3` and Q : R = `1 1/2 : 1 1/3`, find P : R.
Shubham’s age today is 12 years and his father’s is 42 years. Shubham’s mother is younger than his father by 6 years. Find the ratio of Shubham’s mother’s age today to his father’s age today.
Choose the correct answer from the given options :
The ratio of 45 minutes to `5(3)/(4)` hours is
Find the ratio of the following:
33 km to 121 km
Find the ratio of the following:
30 minutes to 45 minutes
