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- Question
- The linear equation such that each point on its graph has an ordinate four times its abscissa is :
Options- A. y + 4x = 0
- B. y = 4x
- C. x = 4y
- D. x + 4y = o
- Correct Answer
- y = 4x
ExplanationLet us assume the abscissa coordinate be x and Ordinate be y.
According to question,
ordinate four times its abscissa
y = 4x
? y - 4x = 0 - 1. Divide 50 into two parts so that the sum of their reciprocals is 1/2.
Options- A. 28,22
- B. 35,15
- C. 20,30
- D. 24,36 Discuss
- 2. Joel purchased 40 notebooks at the rate of ?18 per notebook and 55 pencils at the rate of ? 8 per pencil. What is the total amount that he paid to the shopkeeper?
Options- A. ?1,165
- B. ?1,160
- C. ?1,166
- D. ?1,161 Discuss
- 3. The sum of the two digits of a two-digit number is 15 and the difference between the two digits of the two digit number is 3. What is the product of the two digits of the two digit number?
Options- A. 72
- B. 56
- C. 54
- D. Cannot be determined Discuss
- 4. If the numerator of a fraction is increased by 200% and the denominator is increased by 200% then resultant fraction is 14/5.What is the original fraction?
Options- A. 4/7
- B. 13/12
- C. 11/12
- D. None of these Discuss
- 5. A number is doubled and 9 is added. If the resultant is tripled, it becomes 75. What is the number?
Options- A. 3.5
- B. 6
- C. 8
- D. None of these Discuss
- 6. The cost of 2 sarees and 4 shirts is ? 16000 while 1 saree and 6 shirts cost the same. The cost of 12 shirts is
Options- A. ? 12000
- B. ? 24000
- C. ? 48000
- D. Cannot be determined Discuss
- 7. The system of equations 3x + y - 4 = 0 and 6x + 2y - 8 = 0 has
Options- A. a unique solution x = 1 , y = 1
- B. a unique solution x = 0, y = 4
- C. no solution
- D. infinite solutions Discuss
- 8. If 6x - 10y = 10 and x / (x + y) = 5/7, then (x - y) =?
Options- A. 6
- B. 8
- C. 12
- D. 3 Discuss
- 9. The system of equations 2x + 4y = 6 and 4x + 8y = 6 has
Options- A. exactly two solutions
- B. no solution
- C. infinitely many solutions
- D. a unique solutions Discuss
- 10. In a rare coin collection, there is one gold coin for every three non-gold coins. 10 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1 : 2, Based on the information; the total number of coins in the collection now becomes.
Options- A. 90
- B. 80
- C. 60
- D. 50 Discuss
Linear Equation problems
Search Results
Correct Answer: 20,30
Explanation:
Let us assume the first part is A then second part will be 50 - A.
According to question,
Sum of their reciprocals is 1/2.
1/A + 1/(50 - A) = 1/12
? (50 - A + A)/(50 - A)A = 1/12
? (50)/(50 - A)A = 1/12
? (50) x 12 = 1 x (50 - A)A
? 600 = (50 - A)A
? 600 = 50A - A2
? A2 - 50A + 600 = 0
? A2 - 30A - 20A + 600 = 0
? A(A - 30) - 20(A - 30) = 0
? (A - 30)(A - 20) = 0
? (A - 30) = 0 or (A - 20) = 0
? A = 20 , 30
Correct Answer: ?1,160
Explanation:
According to question,
40 notebooks at the rate of ? 18 per notebook and 55 pencils at the rate of ? 8 per pencil.
Amount paid = ? (40 x 18 + 55 x 8)
Amount paid = ? (720 + 440)
Amount paid = ? 1160
Correct Answer: 54
Explanation:
Let the number be 10x + y where x > y
According to the question.
x + y = 15 ............(1)
and x - y = 3 .........(2)
Add the Equation (1) and (2) , We will get
x + y + x - y = 15 + 3
? 2x = 18
? x = 9
Put the value of x in equation (1). We will get
9 + y = 15
? y = 15 - 9
? y = 6
So we have digits of number x = 9, y = 6
? x * y = 9 * 6 = 54
Correct Answer: None of these
Explanation:
Let us assume the original fraction be x/y.
According to question,
200x/100 / 200y/100 = 14/5
2x/2y = 14/5
?x/y = 14/5
Correct Answer: 8
Explanation:
Let the number be N.
According to question,
A number is doubled and 9 is added then 2N + 9
Again According to question,
If the resultant is tripled, it becomes 75.
3 ( 2N + 9 ) = 75
? 2N + 9 = 25
?2N =16
? N = 8
Correct Answer: ? 24000
Explanation:
Let cost of one saree and shirt be x and y, respectively.
2x + 4y = 16000 ....(i)
x + 6y = 16000 ....(ii)
On multiplying Eq. (ii) by 2 and subtracting from Eq. (i). we get
2x + 4y = 16000
2x + 12y = 32000
-------------------------
-8y = -16000
? y = 2000
Putting the value of y in Eq. (ii), we get
x +6 x 2000 = 16000
? x = 4000
? Cost of 12 shirts = 12y
= 12 x 2000 = ? 24000
Correct Answer: infinite solutions
Explanation:
Given equations of system
3x + y = 4 ...(i)
x + 2y = 8 ...(ii)
Here, a1 = 3 , b2 = 2 and c2 = B
? a1/a2 = b1/b2 = c1/c2 = 1/2
So, the system of equations has infinite solutions, because it represents a parallel line.
Correct Answer: 3
Explanation:
Given, 6x - 10y = 10 ..........(i)
and x/(x + y) = 5/7
? 7x = 5x + 5y
? 2x - 5y = 0 ...(ii)
On multiplying Eq. (ii) by 2 and subtracting from Ed.(i), we get
6x - 10y = 10
4x - 10y = 0
---------------------
2x = 10
? x = 5
Putting the value of x in Eq. (i), we get
30 - 10y = 10
? 10y = 20
? y = 2
? (x - y) = 5 - 2 = 3
Correct Answer: no solution
Explanation:
Given equations 2x + 4y = 6 and 4x + 8y = 6
then,
a1/a2 = 2/4 = 1/2;
b1/b2 = 4/8 = 1/2;
c1/c2 = 6/6 = 1
? a1/b2 = b1/b2 ? c1/c2
So there is no solution for these equations.
Correct Answer: 90
Explanation:
Let the number of gold coins initially be x and the number of non-gold coins be y.
According to the question,
3x = y
When 10 more gold coins, total number of gold coins becomes x + 10 and the number of non-gold coins remain the same at y.
Now, we have 2(x + 10) = y
Solving these two equations, we get
x = 20 and y = 60.
Total number of coins in the collection at the end is equal to
x + 10 + y = 20 + 10 + 60 = 90.
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