Question

47 is divided into two parts in such a way that one-fifth of the first part and one-eighth of the second part are in the ratio 3 : 4. Find the ratio of the two parts.
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Answer 1

let the first part be x and the second part be y

then

x + y = 47 ( equation 1 )

1/5 of first part = x/5

1/8 of second part = y/8

x/5 : y/8 = 3 : 4

or x/5 × 8/y = 3/4

or 8x / 5y = 3/4

or 32x = 15y

or x = 15y/32 ( equation 2 )

from equation 1 and 2

15y/32 + y = 47

or 47y = 47 × 32

or y = 32

and x = 47 - 32

= 15

so, x : y = 15 : 32