Question

If h:k = 2:5, x:y = 3:4 and 2h+x:k+2y = 1:2, find the ratio h-x : k-y

Answer 1

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Answer 2

Given info : If h : k = 2 : 5, x : y = 3 : 4 and 2h+x : k+2y = 1 : 2

To find : The ratio of (h - x) : (k - y) is ...

solution : a/c to question,

h/k = 2/5

so h = 2r and k = 5r (where r is proportional constant)

and x/y = 3/4

so x = 3s and y = 4s (where s is proportional constant)

now, (2h + x)/(k + 2y) = 1/2

⇒(2 × 2r + 3s)/(5r + 2 × 4s) = 1/2

⇒(4r + 3s)/(5r + 8s) = 1/2

⇒8r + 6s = 5r + 8s

⇒3r = 2s ....(1)

now, (h - x)/(k - y)

= (2r - 3s)/(5r - 4s)

= (2r - 3 × 3r/2)/(5r - 2 × 3r) [ from eq (1). ]

= (2r - 9r/2)/(5r - 6r)

= (4r - 9r)/2(-r)

= -5r/-2r

= 5/2

therefore the ratio (h - x) : (k - y) = 5 : 2