Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let the two numbers be x and y.
According to given information, we have
`x/y = (2)/(5)`
⇒ 5x - 2y = 0
⇒ 5x - 2y = 0 ....(i)
And,
`(x + 4)/(y - 32) = (5)/(2)`
⇒ 2x + 8 = 5y - 160
⇒ 2x - 5y = -168 ....(ii)
Multiplying eqn. (i) by 5 and eqn. (ii) by 2, we get
25x - 10y = 0 ....(iii)
4x - 10y = -336 ....(iv)
Subtracting eqn. (iv) from eqn. (iii), we get
21x = 336
⇒ x = 16
⇒ 5(16) - 2y = 0
⇒ 80 - 2y = 0
⇒ 2y = 80
⇒ y = 40
Thus, the numbers are 16 and 40.
APPEARS IN
संबंधित प्रश्न
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
13 + 2y = 9x
3y = 7x
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
`1/5( x - 2 ) = 1/4( 1 - y )`
26x + 3y + 4 = 0
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
`[ x - y ]/6 = 2( 4 - x )`
2x + y = 3( x - 4 )
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 :
11(x - 5) + 10(y - 2) + 54 = 0
7(2x - 1) + 9(3y - 1) = 25
Solve the following simultaneous equation :
8v - 3u = 5uv
6v - 5u = -2uv
Solve the following pairs of equations:
`(x + y)/(xy)` = 2
`(x - y)/(xy)` = 6
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.
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.
