Question

Two numbers are such that the ratio between them is 3 : 5. If each is increased by 10, the ratio between the new numbers so formed is 5 : 7 . Find the original numbers. i need it with prper steps.for my exam

Answer 1

Let the original numbers be x, y. Then original ratio will be x/3 = y/5 or x=3y/5. If we increase both the numbers by 10, then the new ratio will be( x+10)/5= (y+10)7. or 7x+70= 5y+50 I.e. 5y-7x=20. from the above x=3y/5, if we substitute, 5y-7(3y/5)=20, or (25y-21y)/5=20, I.e. 4y=100, y=25, therefore x=3*25/5=15. so the original numbers are 15, 25