Proportions in Division

A relation giving the equality of two ratios in the form a/b=c/d
Previous it was written as a: b: :c:d which has become obsolete these days .here a&d are known as extremes and b&c are known as means. If two ratios are in proposition then the product of extremes must be equal to the product of means. ad=bc, the operation of componenendo. Dividend and converted applied to the proportions a/b =c/d This is known as simple proposition.

Proportions in division Explanation:

Ex 1: C and D earn a profit of   Rs. 6000 in a business. Divide the profit between c and din the ratio 2: 1.
Solution:
Step 1: Amount to be divided = Rs. 6000 in the ratio 2 : 1.
If C gets Rs.2 then D will get Rs. 1.
Step 2: Find the sum of terms of the ratio.
2 + 1 = 3.
For every Rs. 3, C gets Rs. 2 and D gets Re. 1.
Step 3: C’s share of profit = 2 / 3
D’s share of profit = 1/3
C’s share of profit out of Rs. 6000 = ( 2 / 3) x 6000
    = Rs. 4000
  D’s share of profit out of Rs. 6000 = ( 1 / 3) x 6000
   = Rs. 2000C gets Rs. 4000 and D gets Rs. 2000.

Proportions in division Practice problems:

Example1: Divide Rs. 1800 in the ratio (1/2) : (1/4) : (1:/6)
Solution:
We find Proportions in division for this problem
Step 1: Amount to be divided in the ratio 1 /2 : 1 /4 : 1/6= Rs. 1800
Step 2: Simplify the ratio with the help of  L.C.M
 we find the of given ratios
.L.C.M. = 12
Multiply each ratio by 12
 1  /2 × 12 :  1 / 4 ×12  : 1 /6 ×12
= 6 : 3 : 2
Step 3: Divide Rs. 1800 in the ratio 6: 3: 2.

6 +3 +2 = 11
C’s share = 6/12  × 1800
        =1800/2
         =900
        = Rs. 900
D’s share = 3  /12 × 1800
         =1800/4
         = Rs. 450
E’s share = 2  12 × 1800
         =1800/6
        =300
        = Rs. 300
 C gets Rs.900, D gets Rs.450 and E gets Rs.300.

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Example3: Express the following ratios in the form of 1: n.
a) 4:16 
Solution:
We find Proportions in division for this problem
a) 4: 16
Dividing by 4 we get,
4/4  : 16/4
Answer is = 1:4