11 Plus Exams Forum

Hi, could someone help with the following pls:

At the start of the month a shop had 20-inches and 40-inches television sets in the ratio 4:5. By the end of the month, 200 20-inches and 500 40-inches were sold and the ratio of 20-inches to 40-inches tv sets became 1:1. How many tv sets of each type were there at the start of the month?



My answer:
I worked out 1200 and 1500 because the difference is 300 and 300 is also the difference between number of tv of each sets solds so I did 300x4 and 300x5 but Im not sure it is correct and I can't really explain my reasoning.

Suggestions very welcome, many thanks

The 300 extra 40" TVs must be one ninth of the original total (4+ 5 =9)

So 9 x 300 = 2700 TVs originally made up as you said above.

Another way of looking at it:

Your reasoning is right - it might help to try and phrase it slightly differently.

The original ratio is 4:5 (20 inches to 40 inches). So for every 4 20" TVs, they have 5 40" TVs.
So whatever the total number of 20" TVs they have, they have 1/4 more 40" TVs.

Now, after selling 200 20" TVs and 500 40" TVs i.e. 300 more 40" TVs, they have the same amount of each.

SO, they must have originally had 300 more 40" TVs, which we also know is the same as 1/4 of the total number of 20" TVs.

Therefore, the original number of 20" TVs was 4x300=1200 and 40" TVs was 1200+300=1500.

Thanks Guest55 and Maddad, it s very helpful as I was struggling to explain it to ds.