Advertisements
Advertisements
प्रश्न
If x and y be unequal and x: y is the duplicate ratio of (x + z) and (y + z) prove that z is mean proportional between x and y.
उत्तर
Since x : y is duplicate ratio of (x + z) and (y + z)
∴ x : y = (x + z)2 : (y + z)2
x(y + z)2 = y(x + z)2
On simplifying we get
xy2 + xz2 = yx2 + yz2
⇒ x2y - xy2 = xz2 - yz2
⇒ xy(x -y) = z2(x - y)
⇒ xy = z2
⇒ x : z : : z : y.
Hence proved.
APPEARS IN
संबंधित प्रश्न
Calculate the ratio in which the line joining A(−4, 2) and B(3, 6) is divided by point P(x, 3). Also, find
- x
- length of AP.
Find sub-duplicate ratio of 9 : 16
Convert the following percentage to fractions and ratio:
0.25%
If x2, 4 and 9 are in continued proportion, find x.
If A : B = 3 : 5 and B : C = 4 : 7, find A : B : C
How will Rs 31500 be shared between A, B, and C; if A gets the double of what B gets, and B gets the double of what C gets?
The ratio of the number of male and female workers in a textile mill is 5 : 3. If there are 115 male workers, what is the number of female workers in the mill?
Fill in the following blanks:
`15/18 = square/6 = 10/square = square/30`
[Are these equivalent ratios?]
In a college, out of 4320 students, 2300 are girls. Find the ratio of number of boys to the total number of students.
Express `33 1/3%` as a ratio in the lowest term.
