5. Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5. Find the numbers
( Ans: 40, 48 )
Class 10
Content Quality Solution Required
#No Spams
Answers
Let the common ratio be x.
Then the given numbers are 5x and 6x.
Given that if 8 subtracted from each of these numbers, the ratio becomes 4:5.
= > (5x - 8)/(6x - 8) = 4/5
= > 5(5x - 8) = 4(6x - 8)
= > 25x - 40 = 24x - 32
= > 25x - 24x = -32 + 40
= > x = 8.
The 1st number = 5x
= 5 * 8
= 40.
The 2nd number = 6x
= 6 * 8
= 48.
Therefore, the two numbers are 40 and 48.
Hope this helps!
Let the ratio before subtraction be : 5x : 6x
So after subtracting 8 from each of them, the ratio becomes 4 : 5
=> New ratio = 4x : 5x
Hence 5x - 8 + 6x - 8 = 4x + 5x
=> 11x - 16 = 9x
=> 11x - 9x = 16
=> 2x = 16
=> x = 16 / 2 = 8
Hence the old ratio is 5x : 6x = 5 * 8 : 6 * 8 => 40 : 48, which is the required answer.
Hope my answer helped !