Advertisements
Advertisements
Question
If r2 = pq, show that p : q is the duplicate ratio of (p + r) : (q + r).
Advertisements
Solution
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
RELATED QUESTIONS
What quantity must be subtracted from each term of the ratio 9 : 17 to make it equal to 1 : 3?
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 `"a"/"b" = "c"/"d"`, show that: `(a^3c + ac^3)/(b^3d + bd^3) = ("a" + "c")^4/("b" + "d")^4`
Express the following ratios in its simplest form :
48: 54
Find: The sub-triplicate ratio of 216: 343
The ratio of income to savings of a family is 11 : 2. Find the expenditure if the savings is Rs 1520.
One of the terms in a ratio cannot be 1
25 kg : 20 g = 50 kg : 40 g
At the parking stand of Ramleela ground, Kartik counted that there are 115 cycles, 75 scooters and 45 bikes. Find the ratio of the number of cycles to the total number of vehicles.
Find the ratio of the following:
