# 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.

2
by rakeshkasniya77

2016-04-04T12:34:25+05:30
given :
⇒ the two numbers are in the ratio 5:6
⇒ if 8 is subtracted from each the numbers
⇒ the ratio after subtracted will become 4:5

need to find out :
the two numbers used.

solution :
let the 2 number be :
⇒ the first number will be 5s
⇒ the second number will be  6s

" according to the question we need to subtract it with 8 "
⇒ 5s - 8 - let this be A
⇒ 6s - 8 -  let this be B

now again according to the question again :
the ratio of A and B =
⇒
⇒ 25s - 40 = 24s - 32
( now let -32 go to left side and even let 25s go to right side )
⇒ -40 + 32 = 24s - 25s
here I've done direct subtractions and additions
⇒ s = 8
∴ the value of s = 8

the first number = 5s
⇒ 5 * 8 = 40

the second number = 6s
⇒ 6 * 8 = 48
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therefore the first number = 40 and the second number = 48
2016-04-04T12:42:55+05:30
Two no. are in the ratio of 5 ratio 6
let two no. x/y =5/6
from that the eq will become 6x -5y =1    eq 1
according to ques
x-8/y-8=4/5
5(x-8)=4(y-8)
5x -40 =4y- 32
5x-4y = 8            eq 2
multipy eq 1 by 4 and  eq 2 by 5
24x- 20y=0        eq3
25x-20y=40           eq4
subtract  eq 3 fm eq 4
the value of x = 40            eq 5
put eq 5 in eq 1
6(40)-5y =0
y=48
two n. are 40 and 48.............
the method we used is elimination method

plzz mark as bst