Q. A retailer sells a bicycle for $300 after applying a discount of 10%. What was the original price of the bicycle?
A.
$270
B.
$330
C.
$300
D.
$350
Solution
Let the original price be x. After a 10% discount, the selling price is x - (0.10 * x) = 0.90x. Setting this equal to $300 gives 0.90x = $300, so x = $300 / 0.90 = $333.33.
Q. A sequence of numbers is in arithmetic progression. If the first term is 12 and the last term is 48, and there are 8 terms in total, what is the common difference?
A.
4
B.
5
C.
6
D.
3
Solution
The common difference d can be found using the formula for the nth term. The last term is given by a + (n-1)d. Here, 48 = 12 + (8-1)d, solving gives d = 4.
Q. A sequence of numbers is in arithmetic progression. If the first term is 8 and the last term is 32, and there are 6 terms, what is the common difference?
A.
4
B.
5
C.
6
D.
3
Solution
Using the formula for the last term: a + (n-1)d = last term, we have 8 + 5d = 32. Solving gives d = 4.
Q. A shopkeeper sells a shirt for $30 after giving a discount of 20%. What was the original price of the shirt?
A.
$36
B.
$40
C.
$42
D.
$45
Solution
Let the original price be x. After a 20% discount, the selling price is 80% of x. Thus, 0.8x = 30. Solving for x gives x = 30/0.8 = 37.5. Therefore, the original price is $36.
Q. A shopkeeper sells a shirt for $30 after giving a discount of 25%. What was the original price of the shirt?
A.
$40
B.
$35
C.
$45
D.
$50
Solution
Let the original price be x. After a 25% discount, the selling price is x - 0.25x = 0.75x. Setting this equal to $30 gives 0.75x = 30, so x = 30/0.75 = $40.
Q. A shopkeeper sells a shirt for $30, making a profit of 20%. What was the cost price of the shirt?
A.
$25
B.
$20
C.
$24
D.
$22
Solution
Let the cost price be x. The selling price is given by x + 0.2x = 1.2x. Setting this equal to $30 gives us 1.2x = 30, so x = 30/1.2 = 25. Thus, the cost price of the shirt is $25.
Q. A shopkeeper sells a shirt for $30, which is a 20% profit on the cost price. What is the cost price of the shirt?
A.
$24
B.
$25
C.
$26
D.
$27
Solution
Let the cost price be x. The selling price is 30, which is 120% of the cost price. Therefore, 1.2x = 30. Solving for x gives x = 30/1.2 = 25. Thus, the cost price is $25.
Q. A solution contains 20% sugar. If 5 liters of this solution is diluted with 10 liters of water, what is the new percentage of sugar in the solution?
A.
10%
B.
15%
C.
20%
D.
25%
Solution
Initial sugar = 20% of 5 liters = 1 liter. Total volume after dilution = 5 + 10 = 15 liters. New percentage = (1/15) * 100 = 6.67%.
