Question

The ratio between two numbers is 4 : 5. If each number be increased by 3, the ratio becomes 19 : 23. Find the hcf of the numbers.?

Answer 1

Step-by-step explanation:

let first number be X and second be y

A.T.Q

X/y =4/5

X=4y/5 first equation

then , each number increased by 3

X+3/y+3=19/23

23x+69=19y+57

now putting the value of X obtained above in this equation we get

23(4y/5)+69=19y+57

92y/5+69=19y+57

92y/5-19y+69-57=0

92y-95y+60=0

-3y+60=0

3y-60=0

y-20=0

y=20

now,putting the value of y in first equation we get

X=4y/5

x=4(20)/5

X=8

now to find HCF

by EDL we get

20=8(2)+4

8=4(2)+0

therefore,

HCF = 4