Advertisements
Advertisements
Question
If 2 is added to the numerator and denominator it becomes `(9)/(10)` and if 3 is subtracted from the numerator and denominator it becomes `(4)/(5) `Find the fraction.
Advertisements
Solution
Let the fraction be `x/y`.
According to given information, we have
`(x + 2)/(y + 2) = (9)/(10)`
and
`(x - 3)/(y - 3) = (4)/(5)`
⇒ 10x + 20
= 9y + 18
and
5x - 15
= 4y - 12
⇒ 10x - 9y = -2 .....(i)
and
5x - 4y = 3 ....(ii)
Multiplying eqn. (ii) by 2, we get
10x - 8y = 6 ....(iii)
Subtracting eqn. (iii) from eqn. (i), we get
-y = -8
⇒ y = 8
⇒ 10x = -(9) = 6
⇒ 10x - 64 = 6
⇒ 10x = 70
⇒ x = 7
∴ Required fraction = `(7)/(8)`.
APPEARS IN
RELATED QUESTIONS
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
2x − 3y − 3 = 0
`[2x]/3 + 4y + 1/2` = 0
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
13x+ 11y = 70
11x + 13y = 74
Solve :
`[ 7 + x ]/5 - [ 2x - y ]/4 = 3y - 5`
`[5y - 7]/2 + [ 4x - 3 ]/6 = 18 - 5x`
Solve the following simultaneous equations:
41x + 53y = 135
53x + 41y = 147
Solve the following pairs of equations:
`(2)/x + (3)/y = (9)/(xy)`
`(4)/x + (9)/y = (21)/(xy)`
Where x ≠ 0, y ≠ 0
Solve the following pairs of equations:
`(x + y)/(xy)` = 2
`(x - y)/(xy)` = 6
If 10y = 7x - 4 and 12x + 18y = 1 ; find the value of 4x + 6y and 8y - x.
The sum of a two-digit number and the number obtained by reversing the digits is 110 and the difference of two digits is 2. Find the number.
The ratio of two numbers is `(2)/(5)`. If 4 is added in first and 32 is subtracted from the second, the ratio becomes the reciprocal of the original ratio. Find the numbers.
Anil and Sunita have incomes in the ratio 3 : 5. If they spend in the ratio 1 : 3, each saves T 5000. Find the income of each.
