SOLUTION: The ratio of Thomas' total marks to Ken's total marks in the mid-year examination was 4:5. Thomas' marks increased by 50% in the final year examination. How many percent must Ken's

Question 894460: The ratio of Thomas' total marks to Ken's total marks in the mid-year examination was 4:5. Thomas' marks increased by 50% in the final year examination. How many percent must Ken's mark be increased so that their total marks would be equal in the final year examination?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the ratio of tom to ken is 4:5.
tom increases by 50%

the ratio is 4/5.
multiply that by x/x and you get 4x/5x.
this represents the total marks that tom and ken had in the mid-year exam.
it doesn't really matter what the value of x is.
it only matter that, whatever the value of x, the ratio will be the same.
4*5 = 20 divided by 5*5 = 25 and you get 20/25 which is equal to 4/5.
you'll get the same ratio no matter what the value of x is.

tom's marks increase by 50%
since tom's marks are equal to 4x and they increase by 50%, then they increase by 2x for a total of 6x in the final.

in order to get the same score as tom in the final, ken must also score 6x in the final.

ken's score will increase from 5x to 6x.
this is an increase of 1x which is equal to an increase of 20%.

tom increased by 50% from 4x to 6x.
ken increased by 20% from 5x to 6x.

they both have the same mark in the final.

i believe this is what you're asking.

ken's marks have to increase by 20%.

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