Advertisements
Advertisements
Question
If (3x – 4y) : (2x – 3y) = (5x – 6y) : (4x – 5y), find x : y.
Advertisements
Solution
(3x – 4y) : (2x – 3y) = (5x – 6y) : (4x – 5y)
`(3x - 4y)/(2x - 3y) = (5x - 6y)/(4x - 5y)`
Applying componendo and dividendo,
`(3x -4y + 2x - 3y)/(3x - 4y - 2x + 3y) = (5x - 6y + 4x - 5y)/(5x -6y - 4x + 5y)`
`(5x - 7y)/(x - y) = (9x - 11y)/(x - y)`
5x – 7y = 9x – 11y
11y – 7y = 9x – 5x
4y = 4x
`x/y = 1/1`
x : y = 1 : 1
APPEARS IN
RELATED QUESTIONS
Find the compound ratio of 2a : 3b, mn : x2 and x : n
If 15(2x2 – y2) = 7xy, find x : y; if x and y both are positive.
Two positive numbers are in the ratio 3 : 5 and the difference between their squares is 400. Find the numbers.
State true or false :
A ratio of 250 gm and 3 kg is 1 : 12.
Arrange 5: 6, 8: 9, 13: 18 and 7: 12 in ascending order of magnitude.
Find the duplicate ratio of 5a : 6b
Write the following ratio in the simplest form:
1 L 35 mL : 270 mL
0.2 : 5 = 2 : 0.5
In a school, the ratio of the number of large classrooms to small classrooms is 3 : 4. If the number of small rooms is 20, then find the number of large rooms.
Cost of a dozen pens is ₹ 180 and cost of 8 ball pens is ₹ 56. Find the ratio of the cost of a pen to the cost of a ball pen.
