Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
3 - (x - 5) = y + 2
2 (x + y) = 4 - 3y
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
Solve the following simultaneous equations:
41x + 53y = 135
53x + 41y = 147
Solve the following pairs of equations:
`(3)/(2x) + (2)/(3y)` = 5
`(5)/x - (3)/y` = 1
Solve the following pairs of equations:
y - x = 0.8
`(13)/(2(x + y)) = 1`
Solve the following pairs of equations:
`(xy)/(x + y) = (6)/(5)`
`(xy)/(y - x)` = 6
Where x + y ≠ 0 and y - x ≠ 0
In a two-digit number, the sum of the digits is 7. The difference of the number obtained by reversing the digits and the number itself is 9. Find the number.
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 sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes `(1)/(2)`. Find the fraction.
If 1 is added to the denominator of a fraction, the fraction becomes `(1)/(2)`. If 1 is added to the numerator of the fraction, the fraction becomes 1. Find the fraction.
