Advertisements
Advertisements
प्रश्न
If (p – x) : (q – x) be the duplicate ratio of p : q then show that : `1/p + 1/q = 1/x`.
Advertisements
उत्तर
We have,
`(p -x)/(q - x) = p^2/q^2`
`=>` q2(p – x) = p2(q – x)
`=>` pq2 – q2x = p2q – p2x
`=>` p2x – q2x = p2q – pq2
`=>` x(p2 – q2) = pq(p – q)
`=>` x(p – q)(p + q) = pq(p – q)
`=> x = (pq)/(p + q)`
`=> (p + q)/(pq) = 1/x`
`=> p/(pq) + q/(pq) = 1/x`
`=> 1/p + 1/q = 1/x`
APPEARS IN
संबंधित प्रश्न
Two positive numbers are in the ratio 3: 4 and the sum of their squares is 1225. Find the numbers.
The weekly expenses of a boy have increased from ₹ 1,500 to ₹ 2,250. Find the ratio of:
(i) increase in expenses to original expenses.
(ii) original expenses to increased expenses.
(iii) increased expenses to increase in expenses.
Find the fourth proportional of 2.1, 1.5 and 8.4.
Find the ratio of the price of a pencil to that of a ball pen if pencils cost Rs 96 per score and ball pens cost Rs 50.40 per dozen.
From your school diary, write the ratio of the number of holidays to the number of working days in the current academic year
The ratio of the number of sides of a square to the number of edges of a cube is ______.
`3/8 = 15/40`
To find the ratio of two quantities, they must be expressed in _____ units.
Divide 20 pens between Sheela and Sangeeta in the ratio of 3 : 2.
Present age of father is 42 years and that of his son is 14 years. Find the ratio of age of father after 10 years to the age of son after 10 years.
