You are an AI assistant to help me solve math problem.
I first give you an original question with an unknown variable x, then I give you the answer to this original question.
You help me determine the value of x.
Follow the given examples and answer the question.


Question: there were 35 students in a hostel. due to the admission of 7 new students the expenses of the mess were increased by rs . 84 per day while the average expenditure per head diminished by re x. What was the original expenditure of the mess?
Answer Choices: (A) rs 450 (B) rs 920 (C) rs 550 (D) rs . 630 (E) none of these
If we know the answer to the above question is (D) rs . 630, what is the value of unknown variable x?
A:
Let's think step by step.
To find the value of x, we can set up an equation based on the information provided in the question.
Let's denote the original expenditure of the mess as X.
According to the question, the total expenses of the mess increased by rs. 84 per day after the admission of 7 new students. So, the new total expense per day is X + 84.
The average expenditure per head diminished by x, which means the original average expenditure per head was X/35, and the new average expenditure per head is (X + 84)/42 (since there are now 42 students in total).
We can set up the equation as follows:
(X + 84)/42 = X/35 - x
To solve for x, we need to substitute the answer choice (D) rs. 630 for X and solve for x.
(630 + 84)/42 = 630/35 - x
714/42 = 18 - x
17 = 18 - x
x = 18 - 17
x = 1
The value of x is 1.


Question: The average weight of a , b and c is 45 kg. If the average weight of a and b be 40 kg and that of b and c be x kg, then the weight of b is:
Answer Choices: (A) 31 kg (B) 32 kg (C) 33 kg (D) 35 kg (E) none of these
If we know the answer to the above question is (D) 35 kg, what is the value of unknown variable x?
A:
Let's think step by step.
To find the value of x, we can set up equations based on the information provided in the question.
Let's denote the weight of person a as A, the weight of person b as B, and the weight of person c as C.
According to the question, the average weight of a, b, and c is 45 kg, so we can write the equation:
(A + B + C)/3 = 45
The average weight of a and b is 40 kg, so we can write the equation:
(A + B)/2 = 40
The average weight of b and c is x kg, so we can write the equation:
(B + C)/2 = x
From the second equation, we can isolate A and write it as:
A = 80 - B
Substituting A = 80 - B into the first equation, we get:
(80 - B + B + C)/3 = 45
80 + C = 135
C = 135 - 80
C = 55
Substituting C = 55 into the third equation, we get:
(B + 55)/2 = x
xIf we know the answer to the above question is (D) 35 kg, we can substitute B = 35 into the equation and solve for x:
(35 + 55)/2 = x
90/2 = x
x = 45
The value of x is 45.


Question: A trader sells 40 metres of cloth for rs . 8200 at a profit of rs . 35 per metre of cloth. How much profit will the trader earn on x metres of cloth?
Answer Choices: (A) rs . 950 (B) rs . 1500 (C) rs . 1000 (D) rs . 1400 (E) none of these
If we know the answer to the above question is (D) rs . 1400, what is the value of unknown variable x?
A:
Let's think step by step.
To find the value of x, we can set up an equation based on the information provided in the question.
Let's denote the profit on x metres of cloth as P.
According to the question, the trader sells 40 metres of cloth for rs. 8200 at a profit of rs. 35 per metre of cloth. So, the profit on 40 metres of cloth is 35 * 40 = rs. 1400.
We can set up the equation as follows:
P = (Profit on 40 metres of cloth) * (x/40)
To solve for x, we need to substitute the answer choice (D) rs. 1400 for P and solve for x.
1400 = 1400 * (x/40)
Dividing both sides by 1400:
1 = x/40
x = 40
The value of x is 40.


Question: A train x m long passes a man, running at 5 km / hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Answer Choices: (A) 28 km/hr (B) 50 km/hr (C) 77 km/hr (D) 22 km/hr (E) 12 km/hr
If we know the answer to the above question is (C) 77 km/hr, what is the value of unknown variable x?
A:
Let's think step by step.
To find the value of x, we can set up an equation based on the information provided in the question.
Let's denote the speed of the train as T km/hr.
According to the question, the train is x meters long and passes a man running at 5 km/hr in the same direction in which the train is going in 10 seconds.
When a train overtakes a moving object, the relative speed of the train with respect to the object is the difference between their speeds.
The relative speed of the train and the man is T - 5 km/hr (since the train is going in the same direction as the man).
We can convert the speed to meters per second (m/s) to match the distance unit of the train. 1 km/hr = 5/18 m/s.
So, the relative speed of the train and the man is (T - 5) * (5/18) m/s.
The time taken for the train to pass the man is given as 10 seconds.
The distance covered by the train in 10 seconds is the length of the train, which is x meters.
We can use the formula distance = speed * time to set up the equation:
x = (T - 5) * (5/18) * 10
To solve for x, we need to substitute the answer choice (C) 77 km/hr for T and solve for x.
x = (77 - 5) * (5/18) * 10
x = 72 * (5/18) * 10
x = 200 meters
The value of x is 200.


Question: If x / y = 3/4 and 8x + 5y = x,then find the value of a.
Answer Choices: (A) 1/2 (B) 3/2 (C) 5/2 (D) 4/2 (E) 7/2
If we know the answer to the above question is (B) 3/2, what is the value of unknown variable x?
A:
Let's think step by step.
To find the value of x, we can use the given equations and solve for x.
We are given:
x / y = 3/4
8x + 5y = x
To eliminate the variable y, we can rearrange the first equation to express y in terms of x:
y = (4/3)x
Substituting this value of y into the second equation, we get:
8x + 5((4/3)x) = x
8x + (20/3)x = x
(24/3)x + (20/3)x = x
(44/3)x = x
xIf we know the answer to the above question is (B) 3/2, we can substitute x = 3/2 into the equation and solve for x:
(44/3)(3/2) = x
(44/2) = x
22 = x
The value of x is 22.


Question: A person is traveling at x km/hr and reached his destiny in 2.5 hr, then find the distance?
Answer Choices: (A) 53 km (B) 55 km (C) 52 km (D) 60 km (E) 50 km
If we know the answer to the above question is (E) 50 km, what is the value of unknown variable x?
A:
Let's think step by step.
To find the value of x, we can use the given information and solve for the distance traveled.
According to the question, the person is traveling at x km/hr and reaches their destination in 2.5 hours.
The formula to calculate distance is distance = speed * time.
We can substitute the given values into the formula:
Distance = x km/hr * 2.5 hr
Distance = 2.5x km
xIf we know the answer to the above question is (E) 50 km, we can set up the equation and solve for x:
2.5x = 50
Dividing both sides by 2.5:
x = 20
The value of x is 20.


Question: John found that the average of 15 numbers is x. If 10 is added to each number then the mean of the numbers is?
Answer Choices: (A) 50 (B) 45 (C) 65 (D) 78 (E) 64
If we know the answer to the above question is (A) 50, what is the value of unknown variable x?
A:
Let's think step by step.
To find the value of x, we can use the given information and solve for the new mean of the numbers.
According to the question, the average of 15 numbers is x.
We can denote the sum of the 15 numbers as S.
So, the sum of the 15 numbers is 15x.
If 10 is added to each number, the new sum of the numbers is (15x + 1015) because there are 15 numbers and each number has 10 added to it.
The new mean is the new sum divided by the number of numbers, which is 15.
We can set up the equation as follows:
(New sum)/15 = (15x + 1015)/15
To solve for x, we need to substitute the answer choice (A) 50 for the new mean and solve for x:
(15x + 10*15)/15 = 50
(15x + 150)/15 = 50
15x + 150 = 50 * 15
15x + 150 = 750
15x = 750 - 150
15x = 600
x = 600/15
x = 40
The value of x is 40.


Question: A person is traveling at 20 km/hr and reached his destiny in x hr then find the distance?
Answer Choices: (A) 53 km (B) 55 km (C) 52 km (D) 60 km (E) 50 km
If we know the answer to the above question is (E) 50 km, what is the value of unknown variable x?
A:
Let's think step by step.
To find the value of x, we can use the given information and solve for the distance traveled.
According to the question, the person is traveling at 20 km/hr and reaches their destination in x hours.
The formula to calculate distance is distance = speed * time.
We can substitute the given values into the formula:
Distance = 20 km/hr * x hr
Distance = x * 20 km
xIf we know the answer to the above question is (E) 50 km, we can set up the equation and solve for x:
x * 20 = 50
Dividing both sides by 20:
x = 50/20
x = 2.5
The value of x is 2.5.