Question

The ratio of balls in three boxes is 6:8:9. In what ratio should the balls in the second and third boxes be increased, so that the final ratio becomes
1:3:4?​

Answer 1

The ratio in which the balls in the second and third boxes be increased = 2:3.

Step-by-step explanation:

Given: The ratio of balls in three boxes is 6:8:9.

Find: In what ratio should the balls in the second and third boxes be increased, so that the final ratio becomes

1:3:4?​

Solution:  

To change the ratio to 1:3:4, the given ratio will have to change to 6:18:24.

So the second box should contain 18 balls and third box should contain 24 balls.

Since the second box has 8 balls, we need to add 10 balls to it.

Since the third box has 9 balls, we need to add 15 balls to it.  

So, the ratio in which the balls in the second and third boxes be increased =  10:15 = 2:3.

Answer 2

The ratio in which the balls in the second and third boxes be increased is 2 : 3

Step-by-step explanation:

Given

The final ratio is 1 : 3 : 4

Initial ratio is 6 : 8 : 9

Scaling up the final ratio we get

1 : 3 : 4 is same as 6 : 18 : 24

Initial ratio in 2nd and 3rd boxes = 8 : 9

Final ratio = 18 : 24

So balls in the 2nd and 3rd boxes have been increased by 10 and 15 respectively

Thus, the ratio in which they have been increased

= 10/15

= 2/3

Hope this answer is helpful.

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