Ratio and Proportion

 Ratio and Proportion

Ratio: It is the comparison of two like terms in its simplest form. E.g. A:B = 4:5

Proportion: It is an equality between two ratios. In other words, whenever two ratio can be equated, we call it proportion. E.g. A: B = C:D     =  A*D = B*C 

Important Formula:

1.       Product of Extreme  =  Product of mean

A: B = C:D     =  A*D = B*C 

2.    

Question :    Combined ratio:

Given that

A: B =  4: 3   -------------------------------eq1

B: C  = 5:6    -------------------------------eq2

Find  A: B:C  ?

Multiply eq1 with 5  and eq2 with 3

A: B = 20:15

B: C  = 15:18

A: B:C  20:15:18

Note: Ratio between A: B and B: C will remain as it is.

Solved Examples

Q1. A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?

Solution:

C will get 4 parts and D will get 3 parts.

Hence 4-3 = 1 part = Rs 1000.

Now, B will get 2 parts = 2*1000 = 2000.

Q2.

In entrance test the ratio of applicants to successful students was 21: 11. If 1176 students appeared in the test, how many got through it? Solution: Applicant: Successful = 21: 11 In other words, Applicant is 21 parts and Successful is 11 parts. Now, Total applicant ( i.e. 21 parts) = 1176 Then , Successful = 11 parts = (1176*11 )/ 21  =   616. Q3. A, B and C divide an amount of ` 4000 amongst themselves in the ratio of 2:5:1 respectively. If an amount of ` 800 is added to each of their shares, what will be the new ratio of their shares of the amount? Solution: Total Parts of A, B and C = 2+5+1 = 8parts = 4000 Share of each A= 2/8  part = 1000 B= 5/8 part  =2500 C= 1/8 part = 500 Now, when 800 is added to each share New share will become: A’= 1000+800 =1800 B’= 2500+800 =3300 C’ = 500+800  = 1300 Hence New Ratio = A:B:C =  1800: 3300: 1300   = 18:33: 13 Q4. Sita and Gita’s ages are in the ratio of 3:4, Gita and Lata’s ages are in the ratio of 4:7 and Lata and Ram’s ages are in the ratio of 7:9. What is the ratio of Sita’s and Ram’s ages? Solution: Sita: Gita = 3:4 Gita: Lata = 4:7 Lata: Ram = 7:9 Sita: Ram = ? Sita: Ram  = 3:9 = 1:3 Q5. The ratio of length and breadth of a rectangle is 3: 2. If the breadth is increased by 20% and length is increased by 10%, then what will be the new ratio of breadth and length? Solution: length :  breadth =  3part : 2 part after increase length’ = 3.3 part breadth’ = 2.4 part breadth’ length’ =  2.4: 3.3= 24: 33   = 11:8 Q6. A sum of money is divided among A, B, C and D in the ratio 5:8:9:11. If the share of B is ` 2475 more than the share of A then what is the total amount of money of A & C together? Solution: A: B: C: D= 5:8:9:11. A: B: C: D= 5 Part :8 Part:9 Part:11 Part. share of B is ` 2475 more than the share of A means, 8part – 5 Part = 3part = 2475 hence 1 part = 825 now, A & C together= 5+9 = 14 part = 14*825 = 11550.