**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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