Mathematics Therapy

INCREASE AND DECREASE OF A QUANTITY IN A GIVEN RATIO .

If the length of time for carrying out an assignment is increased from 40 minutes to 1 hour , the ratio of the new time to the old time 60:40 = 3:2. So we say that the time has increased in the ratio 3:2
That is, the new time is 3/2 times the old time.
On the other hand , if the length of time is reduced from 54 minutes to 45 minutes, the ratio of the new time to the old time is 45:54 = 5:6, and we say that the time has decreased in the ratio 5:6. That is, the new time is 5/6 times the old time.
The fraction 5/6 by which the old time , 54 minutes must be multiplied to give the new time 45 minutes is called the multiplying factor. i.e
New quantity
---------------------- =
Old quantity
Multiplying factor.
The multiplying factor is greater than 1 when there is an increase in the ratio and the new quantity is greater than the old quantity; it is less than 1 when there is a decrease in the ratio and the new quantity is less than the old quantity.

Example 1:
Increase N 3.50 in the ratio 10: 7
Solution
New amount = N 3.5 × 10
-----
7
= N 5. 00
Example 2:
Decrease 30kg in the ratio 5:6
Decreased weight = 30 × 5
---
6
= 25kg.
Example 3:
In what ratio must a length of 20m be increased to become 35m?
The ratio 35m: 20 = 35:20 =7:4
Therefore, if 20m is increased in the ratio 7:4 , it becomes 35m.
Check: 20 × 7
---- m = 35m.
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