Problem 1 :
Each day ,Robert eats 40% of the pistachios left in his jar at that time. At the end of the second day,27 pistachios remain. How many pistachios were in the jar at the start of the first day?
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?
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?
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?
Problem 5 :
A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?
1. Answer :
Each day, Robert eats 40% of the pistachios left in his jar at that time. At the end of the second day, 27 pistachios remain. How many pistachios were in the jar at the start of the first day?
Let x be the number of pistachios at the start of the first day.
Given : Robert eats 40% of the pistachios left in his jar at that time.
Number of pistachios at the end of the first day :
= (100 - 40)% of x
= 60% of x
= 0.6x
Number of pistachios at the end of the second day :
= (100 - 40)% of 0.6x
= 60% of 0.6x
= 0.36x
Given : At the end of the second day, 27 pistachios remain.
0.36x = 27
Divide both sides by 0.36.
x = 75
There were 75 pistachios in the jar at the start of the first day.
2. Answer :
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%
So, B's salary is 25% more than A's salary.
3. Answer :
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.
4. Answer :
Before decrease in price and increase in sale, let $100 be the price per unit and 100 be the number of units sold.
Then the revenue is
= 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 is
= 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.
5. Answer :
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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