Advertisements
Advertisements
प्रश्न
If `"x"/("b + c - a") =" y" /("c + a - b") = "z"/("a + b - c")` , then prove that each ratio is equal to the ratio of `("x + y+z")/("a + b + c")`
उत्तर
`"x"/("b + c - a") =" y" /("c + a - b") = "z"/("a + b - c") = "k"`
x = k (b + c- a)
Y = k (c+a-b)
z = k (a+b-c)
Now ,
`("x + y+z")/("a + b + c")`
`= ("k"("b + c - a") + "k" ("c + a - b")+ "k" ("a + b - c"))/("a + b + c")`
`= ("k" ("b + c - a + c + a - b + a + b - c"))/("a + b + c")`
`= ("k"("a + b + c"))/("a + b + c") = "k"`
Hence ,
`"x"/("b + c - a") =" y" /("c + a - b") = "z"/("a + b - c") = ("x + y+z")/("a + b + c")`
Proved.
APPEARS IN
संबंधित प्रश्न
If the ratio between 8 and 11 is the same as the ratio of 2x – y to x + 2y, find the value of `(7x)/(9y)`.
A man's monthly inoome is Rs 5,000. He saves every month a minimum of R~ 800. Find the ratio of his:
monthly savings to monthly expenses.
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.
Ten gram of an alloy of metals A and B contains 7.5 gm of metal A and the rest is metal B. Find the ratio between :
(i) the weights of metals A and B in the alloy.
(ii) the weight of metal B and the weight of the alloy.
If x, y, and z are in continued proportion, then which of the following is true:
y : x = y : z
In the example below, find the proportion of the first number to the second.
63, 49
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.
Find the compound ratio of:
(a + b)2 : (a – b )2 ,
(a2 – b2) : (a2 + b2),
(a4 – b4) : (a + b)4
Present age of father is 42 years and that of his son is 14 years. Find the ratio of Present age of father to the present age of son.
Of the 288 persons working in a company, 112 are men and the remaining are women. Find the ratio of the number of men to the total number of persons.
