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Question
Two numbers are in the ratio of 5: 6. If 7 is subtracted from each of the numbers, the ratio becomes 4: 5. Find the numbers.
Solution
Let the two numbers be x and y.
We have been given the ratio of two numbers 5:6
`"x"/"y"=5/6` ........(1)
when 7 is subtracted from each number the ratio becomes 4:5
`("x"-7)/("y"-7) = 4/5`............(2)
6x = 5y
⇒ 6x - 5y = 0 .............(3)
5 (x - 7) = 4(y - 7)
⇒ 5x - 35 = 4y - 28
⇒ 5x - 4y = 7 ..........(4)
Solving (3) and (4) by elimination method
Multiply (3) by 5 and (4) by 6
30 x - 25y = 0 ....................(5)
30 x - 24y = 42 ................(6)
Subtracting (5) from (6)
y = 42
Substitute y = 42 in (3) we get
6x - 5 (42) = 0
⇒ 6x = 210
⇒ x = 35
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