Problem 1 :
John paid $64 for an item after 20% discount. Find the price of the item without discount.
Solution :
Let x be the price of the item without discount.
Given : John paid $64 for the item after 20% discount.
Then, we have
(100 - 20)% of x = 64
0.8x = 64
Divide each side by 0.8.
x = 80
So, the price of the item without discount is $80.
Problem 2 :
If A's salary is 20% less than B's salary. By what percent is B's salary more than A's salary?
Solution :
Let us assume B's salary = $100 ----(1)
Then, A's salary = $80 ----(2)
Now we have to find the percentage increase from (2) to (1).
Difference between (1) and (2) = $20.
Percentage increase from (2) to (1) is
= (20/80) ⋅ 100%
= 25%
Hence, B's salary is 25% more than A's salary.
Problem 3 :
In an election, a candidate who gets 84% of votes is elected by majority with 588 votes. What is the total number of votes polled?
Solution :
Let "x" be the total number of votes polled.
Given : A candidate who gets 84% of votes is elected by majority of 476 votes
From the above information, we have
84% of x = 588 ----> 0.84x = 588
x = 588/0.84
x = 700
Hence, the total number of votes polled 700.
Problem 4 :
When the price of a product was decreased by 10 % , the number sold increased by 30 %. What was the effect on the total revenue?
Solution :
Before decrease in price and increase in sale,
Let us assume that price per unit = $100.
Let us assume that the number of units sold = 100.
Then the total revenue = 100 ⋅ 100 = 10000 ----(1)
After decrease 10 % in price and increase 30 % in sale,
price per unit = $90
number of units sold = 130
Then the total revenue = 90 ⋅ 130 = 11700 ----(2)
From (1) and (2), it is clear that the revenue is increased.
Difference between (1) and (2) = 1700.
Percent increase in revenue is
= (Actual increase/Original revenue) ⋅ 100%
= (1700/10000) ⋅ 100%
= 17 %
Hence, the net effect in the total revenue is 17% increase.
Problem 5 :
A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?
Solution :
In the given two fractions, the denominators are 5 and 3.
Let us assume a number which is divisible by both 5 and 3.
Least common multiple of (5, 3) = 15.
So, let the number be 15.
15 ⋅ 3/5 = 9 ----(1) ----> incorrect
15 ⋅ 5/3 = 25 ----(2) ----> correct
Difference between (1) and (2) is 16.
Percentage error is
= (Actual error/Correct answer) ⋅ 100%
= (16 / 25) ⋅ 100%
= 64%
Hence, the percentage error in the calculation is 64%.
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