A trader sells rice to customers at a profit of 20%. But to his regular customers he charges a profit of only 10%. If he makes an overall profit of 18.18…%, what fraction of his
customers are regular customers?
(A) 2
/9 (B) 9
/11 (C) 2
/11 (D) 2
/7 (E)7
/9
Answers
E part is correct
pls mark it brilliant
Given,
A trader sells rice to his new customers at a profit = 20%
A trader sells rice to his regular customers at a profit = 10%
Overall profit made by the trader = 18.18---%
To find,
The fraction of his total customers who are regular customers.
Solution,
We can simply solve this mathematical problem using the following process:
Let us assume that the trader has a total of x regular customers among his every 100 customers. And also, let us assume that the cost price of the rice that the trader sells to each of his customers is Rs. y.
Mathematically,
Profit percentage = (profit)/(cost price)×100
=> profit earned = (profit percentage)/100 × (cost price)
{Statement-1}
Now, according to the question and statement-1;
Total profit earned by the trader from each of these regular customers
= (profit percentage)/100 × (cost price)
= 10/100 × (y)
= Rs. y/10
So, the total profit earned by the trader from all x regular customers
= x regular customers × Rs. y/10
= Rs. xy/10
{Statement-2}
Similarly,
Total profit earned by the trader from each of these new customers
= (profit percentage)/100 × (cost price)
= 20/100 × (y)
= Rs. y/5
So, the total profit earned by the trader from all (100-x) new customers
= (100-x) new customers × Rs. y/5
= Rs. (100-x)y/5
{Statement-3}
Now, according to the question;
Overall profit made by the trader = 18.18---%
=> (total profit earned from all 100 customers)/(total cost price of all the rice sold)×100 = 18.18---%
=> {(the total profit earned by the trader from all x regular customers) + (the total profit earned by the trader from all (100-x) new customers)/(total cost price of all the rice sold)×100 = 18.18---%
=> {(xy/10) + (100-x)y/5}/(100y)×100 = 18.18---%
=> y{(x/10) + (100-x)/5}/(y) = 18.18---
=> {(x/10) + (100-x)/5} = 18.18---
=> {(x/10) + 2(100-x)/10} = 18.18---
=> {(x/10) + (200-2x)/10} = 18.18---
=> {(200-2x+x)/10} = 18.18---
=> (200-2x+x) = 181.818----
=> 200 - x = 181.818----
=> x = 200 - 181.818----
=> x = 18.1818---
=> number of regular customers = 18.1818---
Now,
The fraction of his total customers who are regular customers
= x/100 = (18.1818---)/100
= 0.181818---- = 2/11
Hence, the fraction of his total customers who are regular customers is equal to 2/11. (Option-C)