A picture is made up of just two colours, red and green. They are used in the ratio 4:3. In the picture, if the ratio of red and green in the lower half of the picture is 2:3, then what is the ratio of red and green in the upper half?
Solution which we have
Total parts = 7 Multiply 7 to ratio lower half. You will get 14:21. So, total number of parts is 35. Then the total number of parts in upper half also 35. If we sum both it is 70.
Then, actual value for the total amount is 40 and 30. If we subtract with lower half, then we will get 26 and 9
Doubts which we have
- Why ratio is summed and multiplied with lower half ratio?
- If we are given the upper half ratio 26 and 9, how this problem would be approached?
- Whether this problem can be approached differently?
- To which questions, we can use this approach?
Both the upper and lower half of the image consists of the same no. pixels that is the same no. red +green (per say) in that particular half . Think of it like you have red and green balls and u fill two halves of the box with them but in different ratios in each of them . considering this in mind ,let say they occur in upper half in ratio x:y , the ratio of red balls in upper half is x:x+y and in the lower half is 2:(2+5) . The average of these ratios is given to us , for red is 4:(4+3) . Solve for x,y using this : x/x+y + 2/5 = 2*(4/7) [as the average of these ratios is 4:7 therefore 2*(4/7)]
Similarly for green : y/x+y + 3/5 = 2*(3/7)
solving u get x=26 , y=9 so x:y is 26:9 . The main point here is the total no of pixels are same and red and green are divided among those pixels in a certain ratio . Hope this solution makes sense xD