Advertisements
Advertisements
Question
If m : n is the duplicate ratio of m + x : n + x; show that x2 = mn.
Advertisements
Solution
`m/n = (m + x)^2/(n + x)^2`
`m/n = (m^2 + x^2 + 2mx)/(n^2 + x^2 + 2nx)`
mn2 + mx2 + 2mnx = m2n + nx2 + 2mnx
mn2 – m2n + mx2 – nx2 = 0
mn(m – n) – x2(m – n) = 0
x2(m – n) = mn(m – n)
x2 = mn
RELATED QUESTIONS
A cistern of milk caitains a mixture of milk and water in the ratio of 11 :4. If the cistern contains 60 litres of milk, how much more water must be added to make the
ratio of milk to water as 11:6 ?
If x2, 4 and 9 are in continued proportion, find x.
Find:
The sub-triplicate ratio of the sub-duplicate ratio of 729x18: 64y6.
The income of a man is increased in the ratio of 10 : 11. If the increase in his income is Rs 600 per month, find his new income.
The ratio of zinc and copper in an alloy is 7 : 9. If the weight of copper in the alloy is 12.6 kg, find the weight of zinc in it.
If (7p + 3q) : (3p – 2q) = 43 : 2 find p : q.
The ratio of 8 books to 20 books is ______.
The number of milk teeth in human beings is 20 and the number of permanent teeth is 32. Find the ratio of the number of milk teeth to the number of permanent teeth.
Present age of father is 42 years and that of his son is 14 years. Find the ratio of age of father to the age of son when father was 30 years old.
225% is equal to ______.
