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- Question
- Deepak has some hens and some goats. If the total number of animal heads is 90 and the total number of animal feet is 248, what is the total number of goats Deepak has?
Options- A. 32
- B. 36
- C. 34
- D. Cannot be determined
- Correct Answer
- 34
ExplanationLet hens = H, goats = G
According to the question,
H + G = 90 ...(i)
2H + 4G = 248 ...(ii)
On multiplying Eq. (i) by 2 and subtracting from Eq. (ii) , we get
2H + 2G = 180
2H + 4G = 248
-------------------
-2G = -68
? G = 34 - 1. solve 6x + 3y = 7xy and 3x + 9y = 11xy.
Options- A. x=1, y=3/2
- B. x=-1, y = 3/2
- C. x=3/2, y=1/2
- D. x=1, y= -3/2 Discuss
- 2. if 3 x + y = 81 and 81 x - y = 3, then what is the value of x?
Options- A. 17/16
- B. 17/8
- C. 17/4
- D. 15/4 Discuss
- 3. If x + y - 7 = 0 and 3x + y - 13 = 0, then what is 4x 2 + y 2 + 4xy equal to?
Options- A. 75
- B. 85
- C. 91
- D. 100 Discuss
- 4. If 3x + 7y = 75 and 5x - 5y = 25, what is the value of x + y?
Options- A. 14
- B. 15
- C. 16
- D. 17 Discuss
- 5. If 2x + 3y = 29 and y = x + 3, what is the value of x?
Options- A. 4
- B. 5
- C. 6
- D. 7 Discuss
- 6. The sum of the two digits is 15 and the difference between them is 3. What is the product of the digits?
Options- A. 56
- B. 63
- C. 42
- D. Cannot be determined Discuss
- 7. The numerator of a fraction is 6x + 1 and the denominator is 7 - 4x, x can have any value between -2 and 2, both included. The values of x for which the numerator is greater
Options- A. 3/5 < x ? 2
- B. 3/5 ? x ? 2
- C. 0 < x ? 2
- D. -2 ? x < 2 Discuss
- 8. If (x/4) + (y/3) = 10/24 and (x/2) + y = 1, then the value of x + y is
Options- A. 1
- B. 3/2
- C. 2
- D. 4 Discuss
- 9. The cost of 21 pencil and 9 clippers is ? 819. What is the total cost of 7 pencils and 3 clippers together?
Options- A. ? 204
- B. ? 409
- C. ? 273
- D. ? 208 Discuss
- 10. The value of k for which kx + 3y - k + 3 = 0 and 12x + ky = k, have infinite solutions, is
Options- A. 0
- B. -6
- C. 6
- D. 1 Discuss
Linear Equation problems
Search Results
Correct Answer: x=1, y=3/2
Explanation:
Given equation are 6x + 3y = 7xy
? (6/y) + (3/x) = 7 .....(i)
And 3x + 9y = 11xy
? (3/y) + (9/x) = 11 .....(ii)
On multiplying Eq. (ii) by 2 and subtracting from Eq. (i), we get
(6/y) + (3/x) = 7
(6/y) + (18/x) = 22
-------------------------
- 15/x = - 15
? x = 1
On putting this value in Eq. (i), we get
(6/y) + 3 = 7
? 6/y = 4
? y = 6/4 = 3/2
Correct Answer: 17/8
Explanation:
Given, 3x + y = 81
? 3x + y = 34
? x + y = 4 ...(i)
and 81x - y = 3 or (34)x - y = 3
? x - y = 1/4
On solving the Eqs. (i) and (ii), we get
2x = 17/4 ? x = 17/8
Correct Answer: 100
Explanation:
we have, x + y - 7 = 0
? x + y = 7 ...(i)
and 3x + y - 13 = 0
? 3x + y = 13 ..(ii)
By subtracting Eq. (i) from Eq. (ii), we get
3x + y = 13
x + y = 7
----------------------
2x = 6 ...(ii)
? x = 3
On putting the value of x in Eq. (i), we get
3 + y = 7
? y = 4
Now, 4x2 + y2 + 4xy
= 4 x (3)2 + (4)2 + 4 x 3 x 4
= 4 x 9 + 16 + 48
= 36 + 16 + 48 = 100
Correct Answer: 17
Explanation:
3x + 7y = 75 ..(i)
5x - 5y = 25
? x - y = 5 ...(ii)
On multiplying Eq. (ii) by 7 and adding to Eq. (i), we get
3x + 7y = 75
7x - 7y = 35
------------------
10x = 110
x = 11
? Putting the value of x in Eq. (ii), we get
11 - y = 5
? y = 6
? x + y = 6 + 11 = 17
Correct Answer: 4
Explanation:
2x + 3y = 29 ...(i)
and y = x + 3 ...(ii)
Putting the value of y from Eq. (ii) to Eq. (i), we get
2x + 3y = 29
2x + 3(x + 3) = 29
2x + 3x + 9 = 29
? 5x = 20
? x = 4
Correct Answer:
Explanation:
Let the number be x and y.
Then, according to the question,
x + y = 15 ...(1)
x - y = 3 ...(ii)
on adding Eqs. (i) and (ii), we get
2x = 18
? x = 9
On putting the value of in Eq. (i), we get
y = 6
? Product = xy = 54
Correct Answer: 3/5 < x ? 2
Explanation:
6x + 1 > 7 - 4x
? x > 3/5
? 3/5 < x ? 2
Correct Answer: 3/2
Explanation:
Given, (x/4) + (y/3) = 10/24
? (3x + 4y)/12 = 10/24
? 3x + 4y = 5 ...(i)
and (x/2) + y = 1
x + 2y = 2 ...(ii)
On multiplying Eq. (ii) by 2 and subtracting from Eq. (i).
3x + 4y = 5
2x + 4y = 4
- - -
--------------------------
x = 1
On putting the value of x in Eq. (ii), we get
x + 2y = 2
? 1 + 2y = 2
? y = 1/2
? x + y = 1 + 1/2 = 3/2
Correct Answer: ? 273
Explanation:
Let cost of 1 pencil and 1 clipper be p and c, respectively.
Now, according to the question,
21p + 9c = ? 819
? 3(7p + 3c) = ? 819
? 7p + 3c = ? 273
Cost of 7 pencil and 3 clippers = ? 273
Correct Answer: 6
Explanation:
For infinite solution
a1/a2 = b1/2 = c1/c2
? K/12 = 3/K = (-K + 3)/ -K
? K/12 = 3/K
? K2 = 36
? K = ?36 = 6
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