Ratio, proportion & percentage

1. RATIO, PROPORTION & PERCENTAGE

2. This chapter contains following topics
Ratio
Continued ratio (Combined ratio)
Dividing a quantity in a given ratio
Proportion
Direct Proportion
Inverse Proportion
Compound Proportion
Percentage

3. In this lecture we learn how to find
1-selling price,
2-cost price,
3-profit or loss and
4-percentage of profit or loss
Where
S = Selling price
C = Cost price
r = rate of profit or rate of loss

4. In case of profit we use the following formulae
𝑆 = 𝐶 1 + 𝑟
𝐶 =
𝑆
1+𝑟
Profit = S – C
% 𝑜𝑓 𝑝𝑟𝑜𝑓𝑖𝑡 =
S – C
𝐶
× 100

5. In case of loss we use the following formulae
𝑆 = 𝐶 1 − 𝑟
𝐶 =
𝑆
1−𝑟
Loss = C – S
% 𝑜𝑓 𝑙𝑜𝑠𝑠 =
C – S
𝐶
× 100

6. Example-26
The cost price of an item is
Rs.500. Find the selling price if it
is sold at 25% profit also find
profit.

7. Solution
C = Rs.500
Profit = r = 25% =
25
100
= 0.25
We know that
𝑆 = 𝐶 1 + 𝑟
𝑆 = 500 1 + 0.25
𝑆 = 500 1.25
𝑆 = 𝑅𝑠 625
Profit = S – C
Profit = 625 – 500
Profit = Rs.125

8. Example-27
If the selling price of an item is
Rs.625. Find the cost price if it is
sold at 25% profit on sale.

9. Solution
S = Rs.625
Profit = r = 25% =
25
100
= 0.25
We know that
𝐶 =
𝑆
1+𝑟
𝐶 =
625
1+0.25
𝐶 =
625
1.25
𝐶 = 𝑅𝑠. 500

10. Example-28
The costing an item is Rs.500 is
sold for Rs.625. Find the profit and
percentage of profit.

11. Solution:
S = Rs.625
C = Rs.500
Profit = S – C
Profit = Rs.125
% 𝑜𝑓 𝑝𝑟𝑜𝑓𝑖𝑡 =
S – C
𝐶
× 100
% 𝑜𝑓 𝑝𝑟𝑜𝑓𝑖𝑡 =
625 – 500
500
× 100
% 𝑜𝑓 𝑝𝑟𝑜𝑓𝑖𝑡 =
125
500
× 100
% 𝑜𝑓 𝑝𝑟𝑜𝑓𝑖𝑡 = 25%

12. Example-29
The cost price of an item is Rs.500.
find the selling price if it is sold at
25% loss, also find loss.

13. Solution:
C = Rs.500
Loss = r = 25% =
25
100
= 0.25
We know that
𝑆 = 𝐶 1 − 𝑟
𝑆 = 500 1 − 0.25
𝑆 = 500 0.75
𝑆 = 𝑅𝑠 375
Loss = C – S
Loss = 500 – 375
Loss = Rs 125

14. Example-30
If the selling price of an item is
Rs.375, find the cost price, if it is sold
at 25% loss.

15. Solution:
S = Rs.375
Loss = r = 25% =
25
100
= 0.25
We know that
𝐶 =
𝑆
1−𝑟
𝐶 =
375
1−0.25
𝐶 =
375
0.75
𝐶 = 𝑅𝑠. 500

16. Example-31
The costing of an item is Rs.500 is
sold for Rs.375. Find the loss and
percent of loss.

17. Solution:
S = Rs.375
C = Rs.500
Loss = C – S
Loss = 500 – 375
Loss = Rs.125
% 𝑜𝑓 𝑙𝑜𝑠𝑠 =
C – S
𝐶
× 100
% 𝑜𝑓 𝑙𝑜𝑠𝑠 =
500 – 375
500
× 100
% 𝑜𝑓 𝑙𝑜𝑠𝑠 =
125
500
× 100
% 𝑜𝑓 𝑙𝑜𝑠𝑠 = 25%