Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let the numerator and denominator of a fraction be x and y respectively.
∴ Fraction = `x/y`
According to given information, we have
`(x)/(y + 1) = (1)/(2)`
⇒ 2x = y + 1
⇒ 2x - y = 1 ....(i)
Also,
`(x + 1)/y = 1`
⇒ x + 1 = y
⇒ x - y = -1 ....(ii)
Subtracting eqn. (ii) from (i), we get
x = 2
⇒ 2 - y = -1
⇒ y = 3
∴ Required fraction = `(2)/(3)`.
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
Solve for x and y :
`[ y + 7 ]/5 = [ 2y - x ]/4 + 3x - 5`
`[ 7 - 5x ]/2 + [ 3 - 4y ]/6 = 5y - 18`
Solve for x and y:
4x = 17 - `[ x - y ]/8`
2y + x = 2 + `[ 5y + 2 ]/3`
Solve :
11(x - 5) + 10(y - 2) + 54 = 0
7(2x - 1) + 9(3y - 1) = 25
Solve the following simultaneous equations :
2(3u - v) = 5uv
2(u + 3v) = 5uv
Solve the following pairs of equations:
`(3)/(2x) + (2)/(3y)` = 5
`(5)/x - (3)/y` = 1
Solve the following pairs of equations:
`(3)/x - (1)/y` = -9
`(2)/x + (3)/y` = 5
If 10y = 7x - 4 and 12x + 18y = 1 ; find the value of 4x + 6y and 8y - x.
In a triangle, the sum of two angles is equal to the third angle. If the difference between these two angles is 20°, determine all the angles.
A solution containing 12% alcohol is to be mixed with a solution containing 4% alcohol to make 20 gallons of solution containing 9% alcohol. How much of each solution should be used?
