Advertisements
Advertisements
Question
If `(7"m" + 2"n")/(7"m" - 2"n") = 5/3` use properties of proportion to find:
(i) m : n
(ii) `("m"^2 + "n"^2)/("m"^2 - "n"^2)`
Advertisements
Solution
(i) `(7"m" + 2"n")/(7"m" - 2"n") = 5/3`
Pplying Componendo and dividendo, we get
`(7"m" + 2"n" + 7"m" - 2"n")/(7"m" - 2"n"- 7"m" + 2"n") = (5 + 3)/(5 - 3)`
⇒ `(14"m")/(4"n") = 8/2`
⇒ `"m"/"n" = (8 xx 4)/(2 xx 14)`
⇒ `"m"/"n" = 8/7`
⇒ m : n = 8 : 7
(ii) From i,
`"m"/"n" = 8/7`
⇒ `"m"^2/"n"^2 = 64/49`
Pplying Componendo and Dividendo,we get
`("m"^2 + "n"^2)/("m"^2 - "n"^2) = (64 + 49)/(64 - 49)`
⇒ `("m"^2 + "n"^2)/("m"^2 - "n"^2) = (64 + 49)/(64 - 49)`
⇒ `("m"^2 + "n"^2)/("m"^2 - "n"^2) = 113/15 = 7 8/15`
RELATED QUESTIONS
Which of the following ratio is greater ?
`5/2 : 15/4` and `5/3 : 11/6`
In an examination the ratio of the number of suo:essful candidates to unsuccessful candidates is 7:5. Had 30 more appeared and 10 more passed, the ratio of successful candidates to unsuccessful candidates would have been 4:3. Find the number of candidates who appeared in the examination originally.
If (a – x) : (b – x) be the duplicate ratio of a: b show that:
`(1)/x = (1)/a + (1)/b.`
Express the given ratio in its simplest form: `1 1/3:2 1/4:2 1/2`
Check whether the following quantities form a proportion or not?
3x, 7x, 24 and 56
Find the third proportional of `1/7 "and" 3/14`
Find the value of x, when 2.5 : 4 = x : 7.5.
Find the mean proportion between 3 and 27
If (4x2 + xy) : (3xy – y2) = 12 : 5, find (x + 2y) : (2x + y).
Express the following ratio in the simplest form:
186 : 403
