Advertisements
Advertisements
प्रश्न
If r2 = pq, show that p : q is the duplicate ratio of (p + r) : (q + r).
Advertisements
उत्तर
Given, r2 = pq
Duplicate ratio of (p + r) : (q + r)
= (p + r)2 : (q + r)2
= (p2 + r2 + 2pr) : (q2 + r2 + 2qr)
= (p2 + pq + 2pr) : (q2 + pq + 2qr)
= p(p + q + 2r) : q(q + p + 2r)
= p : q
Thus, p : q is the duplicate ratio of (p + r) : (q + r).
APPEARS IN
संबंधित प्रश्न
If x = `"pab"/("a + b")`, then prove that `("x + pa")/("x - pa") + ("x + pb")/("x - pb") = (2("a"^2 - "b"^2))/"ab"`
If x and y both are positive and (2x2 – 5y2) : xy = 1 : 3, find x : y.
The ratio between the prices of a scooter and a refrigerator is 4 : 1. If the scooter costs ₹ 45,000 more than the refrigerator, find the price of the refrigerator.
Show that 2, 12 and 72 are in continued proportion.
Express the following ratio in the simplest form:
480 : 384
Write the following ratio in the simplest form:
Rs 6.30 : Rs 16.80
The ratio of zinc and copper in an alloy is 7 : 9. If the weight of copper in the alloy is 11.7 kg find the weight of zinc in it.
If `a/b = c/d = e/f`, prove that each ratio is `[(2a^3 + 5c^3 + 7e^3)/(2b^3 + 5d^3 + 7f^3)]^(1/3)`
Which pair of ratios are equal? And why?
`4/5, 12/50`
Out of 1800 students in a school, 750 opted basketball, 800 opted cricket and remaining opted table tennis. If a student can opt only one game, find the ratio of number of students who opted cricket to the number of students opting basketball.
