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All questions of Word Problems for Class 10 Exam
The product of x and y is 36. If both x and y are integers, then what is the least possible value of x - y?- a)-37
- b)-36
- c)-35
- d)-9
Correct answer is option 'C'. Can you explain this answer?
The product of x and y is 36. If both x and y are integers, then what is the least possible value of x - y?
a)
-37
b)
-36
c)
-35
d)
-9
 | Dugard Lekeugo answered |
The least possible value of x-y will just be the difference between the maximum and minimum factor. Thus since min is 1 and max 36, their difference will then be 1-36=-35 which is [C]
A farmer cuts a 300 foot fence into two pieces of different sizes. The longer piece should be four times as long as the shorter piece. How long are the two pieces?- a)70
- b)80
- c)90
- d)60
Correct answer is option 'D'. Can you explain this answer?
A farmer cuts a 300 foot fence into two pieces of different sizes. The longer piece should be four times as long as the shorter piece. How long are the two pieces?
a)
70
b)
80
c)
90
d)
60
 | Ayesha Joshi answered |
x + 4x = 300
Combining the like terms on the left, we get
5x = 300
Dividing by 5, we obtain that
x = 300/5 = 60
Therefore, the shorter piece has a length of 60 feet, while the longer piece has four times this length, that is 4 × 60 feet = 240 feet.
Combining the like terms on the left, we get
5x = 300
Dividing by 5, we obtain that
x = 300/5 = 60
Therefore, the shorter piece has a length of 60 feet, while the longer piece has four times this length, that is 4 × 60 feet = 240 feet.
If a circle has circumference 4in, what is its radius?- a) 0.45in
- b) 0.54in
- c) 0.33in
- d) 0.63in
Correct answer is option 'D'. Can you explain this answer?
If a circle has circumference 4in, what is its radius?
a)
0.45in
b)
0.54in
c)
0.33in
d)
0.63in
 | Michael Carter answered |
To find the radius of a circle, we can use the formula for the circumference of a circle:
C = 2πr
where C is the circumference and r is the radius.
Given that the circumference of the circle is 4 inches, we can substitute this value into the formula:
4 = 2πr
To solve for r, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 2π:
4 / (2π) = r
Simplifying the right side gives us:
2 / π = r
Therefore, the radius of the circle is 2 / π inches, which is approximately 0.6366 inches.
The answer given in option 'D' is 0.63 inches, which is a rounded approximation of 0.6366 inches. Therefore, option 'D' is the correct answer.
C = 2πr
where C is the circumference and r is the radius.
Given that the circumference of the circle is 4 inches, we can substitute this value into the formula:
4 = 2πr
To solve for r, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 2π:
4 / (2π) = r
Simplifying the right side gives us:
2 / π = r
Therefore, the radius of the circle is 2 / π inches, which is approximately 0.6366 inches.
The answer given in option 'D' is 0.63 inches, which is a rounded approximation of 0.6366 inches. Therefore, option 'D' is the correct answer.
If a factory can manufacture b computer screens in n days at a cost of c dollars per screen, then which of the following represents the total cost, in dollars, of the computer screens that can be manufactured, at that rate, in m days?- a)bcm/n
- b)bmn/c
- c)mn/bc
- d)bc/mn
Correct answer is option 'A'. Can you explain this answer?
If a factory can manufacture b computer screens in n days at a cost of c dollars per screen, then which of the following represents the total cost, in dollars, of the computer screens that can be manufactured, at that rate, in m days?
a)
bcm/n
b)
bmn/c
c)
mn/bc
d)
bc/mn
 | Fredrick Acheampong answered |
A
Carlos began with twice as much money as David had. After Carlos gave $12 to David, Carlos still had $10 more than David. How much money did they have combined at the start?- a)$34
- b)$68
- c)$102
- d)$108
Correct answer is option 'C'. Can you explain this answer?
Carlos began with twice as much money as David had. After Carlos gave $12 to David, Carlos still had $10 more than David. How much money did they have combined at the start?
a)
$34
b)
$68
c)
$102
d)
$108
 | Grace Phillips answered |
Analysis:
Let's first represent the amount of money Carlos and David had at the start.
Let x be the amount of money David had.
Carlos had twice as much money as David, so Carlos had 2x at the start.
After Carlos gave $12 to David, Carlos had 2x - 12 and David had x + 12.
Given information:
- After giving $12 to David, Carlos still had $10 more than David. This can be represented as:
2x - 12 = (x + 12) + 10
Solving the equation:
2x - 12 = x + 22
2x - x = 22 + 12
x = 34
Calculating the total amount at the start:
David had $34 at the start
Carlos had 2x = 2(34) = $68 at the start
Combined amount at the start = 34 + 68 = $102
Therefore, the correct answer is option C ($102).
Let's first represent the amount of money Carlos and David had at the start.
Let x be the amount of money David had.
Carlos had twice as much money as David, so Carlos had 2x at the start.
After Carlos gave $12 to David, Carlos had 2x - 12 and David had x + 12.
Given information:
- After giving $12 to David, Carlos still had $10 more than David. This can be represented as:
2x - 12 = (x + 12) + 10
Solving the equation:
2x - 12 = x + 22
2x - x = 22 + 12
x = 34
Calculating the total amount at the start:
David had $34 at the start
Carlos had 2x = 2(34) = $68 at the start
Combined amount at the start = 34 + 68 = $102
Therefore, the correct answer is option C ($102).
Due to inflation, the price of a loaf of bread has increased by 5%. How much does the loaf of bread cost now, when its price was $2.40 last year?- a)3.54
- b)2.52
- c)5.52
- d)6.54
Correct answer is option 'B'. Can you explain this answer?
Due to inflation, the price of a loaf of bread has increased by 5%. How much does the loaf of bread cost now, when its price was $2.40 last year?
a)
3.54
b)
2.52
c)
5.52
d)
6.54
 | Sydney Jenkins answered |
Given:
- Price of a loaf of bread last year = $2.40
- Inflation rate = 5%
To find:
- The current cost of the loaf of bread
Solution:
Step 1: Calculate the increase in the price of the loaf of bread
- Increase = (Inflation rate/100) * Price of the loaf of bread last year
- Increase = (5/100) * $2.40
- Increase = $0.12
Step 2: Calculate the current cost of the loaf of bread
- Current cost = Price of the loaf of bread last year + Increase
- Current cost = $2.40 + $0.12
- Current cost = $2.52
Therefore, the current cost of the loaf of bread is $2.52.
Hence, the correct answer is option B) $2.52.
- Price of a loaf of bread last year = $2.40
- Inflation rate = 5%
To find:
- The current cost of the loaf of bread
Solution:
Step 1: Calculate the increase in the price of the loaf of bread
- Increase = (Inflation rate/100) * Price of the loaf of bread last year
- Increase = (5/100) * $2.40
- Increase = $0.12
Step 2: Calculate the current cost of the loaf of bread
- Current cost = Price of the loaf of bread last year + Increase
- Current cost = $2.40 + $0.12
- Current cost = $2.52
Therefore, the current cost of the loaf of bread is $2.52.
Hence, the correct answer is option B) $2.52.
The symbol Ω represents one of the fundamental operators: +, -, ×, or ÷. If (x Ω y) × (y Ω x) = 1 for all positive values of x and y, then Ω can represent- a)+
- b)x
- c)-
- d)÷
Correct answer is option 'D'. Can you explain this answer?
The symbol Ω represents one of the fundamental operators: +, -, ×, or ÷. If (x Ω y) × (y Ω x) = 1 for all positive values of x and y, then Ω can represent
a)
+
b)
x
c)
-
d)
÷
 | Violet Powell answered |
The symbol "+" represents addition in mathematics. It is used to indicate that two or more numbers or quantities should be added together. For example, in the equation 2 + 3 = 5, the "+" symbol is used to show that the numbers 2 and 3 should be added together to give the result of 5.
If 4 blocks weigh 28 ounces, how many blocks weigh 70 ounces?- a)10
- b)20
- c)25
- d)30
Correct answer is option 'A'. Can you explain this answer?
If 4 blocks weigh 28 ounces, how many blocks weigh 70 ounces?
a)
10
b)
20
c)
25
d)
30
 | Rajeev Kumar answered |
We denote the weight of a block by x. If 4 blocks weigh 28, then a block weighs x = 28/4 = 7
How many blocks weigh 70? Well, we only need to find 70/7 = 10. So, the answer is 10.
On a typical day, a restaurant sells n grilled cheese sandwiches for p dollars each. Today, however, the manager reduced the price of grilled cheese sandwiches by 30% and as a result sold 50% more of them than usual. Which of the following represents the revenue for today’s grilled cheese sandwich sales, in dollars?- a)0.5np - 0.3
- b)1.05np
- c)1.20np
- d)1.50np
Correct answer is option 'B'. Can you explain this answer?
On a typical day, a restaurant sells n grilled cheese sandwiches for p dollars each. Today, however, the manager reduced the price of grilled cheese sandwiches by 30% and as a result sold 50% more of them than usual. Which of the following represents the revenue for today’s grilled cheese sandwich sales, in dollars?
a)
0.5np - 0.3
b)
1.05np
c)
1.20np
d)
1.50np
 | Caleb Taylor answered |
Let's assume that the restaurant typically sells x grilled cheese sandwiches on a typical day.
The revenue on a typical day would be p*x.
After reducing the price by 30%, the new price of each grilled cheese sandwich would be 0.7p.
With the reduced price, the restaurant sold 50% more grilled cheese sandwiches than usual, which is 1.5x.
So, the revenue for today would be (0.7p)*(1.5x) = 1.05px - which is 105% of the revenue on a typical day.
Therefore, the revenue for today is represented by the expression 1.05px.
The revenue on a typical day would be p*x.
After reducing the price by 30%, the new price of each grilled cheese sandwich would be 0.7p.
With the reduced price, the restaurant sold 50% more grilled cheese sandwiches than usual, which is 1.5x.
So, the revenue for today would be (0.7p)*(1.5x) = 1.05px - which is 105% of the revenue on a typical day.
Therefore, the revenue for today is represented by the expression 1.05px.
To complete a job, three workers get paid at a rate of $12 per hour. If the total pay for the job was $180, then how many hours did the three workers spend on the job?- a)5
- b)6
- c)7
- d)8
Correct answer is option 'A'. Can you explain this answer?
To complete a job, three workers get paid at a rate of $12 per hour. If the total pay for the job was $180, then how many hours did the three workers spend on the job?
a)
5
b)
6
c)
7
d)
8
| | Rajeev Kumar answered |
We denote the number of hours by x. Then the total price is calculated as the price per hour ($12) times the number of workers times the number of hours (3). We obtain the equation
12 ⋅ 3 ⋅ x = 180
Simplifying this yields
36x = 180
Dividing by 36 gives
x = 180/36 = 5
Therefore, the three workers needed 5 hours for the job.
12 ⋅ 3 ⋅ x = 180
Simplifying this yields
36x = 180
Dividing by 36 gives
x = 180/36 = 5
Therefore, the three workers needed 5 hours for the job.
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