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- Question
- The sum of the squares of two numbers is 234 and the square of their difference is 144. Find the product of the two numbers?
Options- A. 28
- B. 52
- C. 36
- D. 45
- Correct Answer
- 45
ExplanationLet the two numbers be x and y.
Then, x2 + y2 = 234 ...(i)
and (x - y)2 = 144 ...(ii)
Now, (x - y)2 = 144
? x2 + y2 - 2xy = 144
? 234 - 2xy = 144 [using Eq.(i)]
On substituting the value of x2 + y2 from Eq.(i) in Eq.(ii),
we get
2xy = 90
? xy = 45
So, the product of the two numbers is 45. - 1. If the price of a book when reduced by Rs. 5,a person can buy 2 more books for Rs. 200. Find the original price of the book?
Options- A. Rs. 25
- B. Rs. 30
- C. Rs. 20
- D. Rs. 15 Discuss
- 2. In a rare coins collection, there is one gold coins 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
- 3. A person has only ? 1 and ? 2 coins with him. If the total number of coins that he has is 50 and the amount of money with him is 75, then the number of coins ? 1 and ? 2, respectively are?
Options- A. 15 and 35
- B. 35 and 15
- C. 30 and 20
- D. 25 and 25 Discuss
- 4. In an examination consisting of 60 questions, three marks are given for every correct answer and one mark is deducted for every wrong answer. A student attempts all the questions and gets 120 marks. How many questions did he mark correct?
Options- A. 45
- B. 42
- C. 15
- D. 18 Discuss
- 5. A two-digit number is such that the ten's digit exceeds twice the unit's digit by 2 and the number obtained by interchanging the digits is 5 more than three times the sum of the digits. Find the two-digits number?
Options- A. 83
- B. 38
- C. 56
- D. 65 Discuss
- 6. The degree of polynomial p(x) = x 3 + 1 + 2x = 6x + 1/x is?
Options- A. 2
- B. 4
- C. 3
- D. 5 Discuss
- 7. A piece of cloth cost ? 120. If the piece, then was 2 m longer and each metre of cloth costs ? 2 less than cost of the piece of cloth would have remained unchanged. What is the original rate per metre of the cloth?
Options- A. ? 12
- B. ? 15
- C. ? 10
- D. ? 8 Discuss
- 8.
If ?0.03 x 0.3 a = 0.03 x 0.3 x ? b then value of a is b
Options- A. 0.009
- B. 0.9
- C. 0.09
- D. 0.08 Discuss
- 9. Area of the triangle formed by the graph of the line 2x ? 3y + 6 = 0 along with the coordinate axes is:
Options- A. 1 sq. units 2
- B. 3 sq. units 2
- C. 3 sq. units
- D. 6 sq. units Discuss
- 10. If the distance between two points (0,?5) and (x,0) is 13 unit, then x =
Options- A. 10
- B. ± 10
- C. 12
- D. ± 12 Discuss
Elementary Algebra problems
Search Results
Correct Answer: Rs. 25
Explanation:
Let the original price of the book be Rs. x.
? Number of books bought for Rs.200 = 200/x
and reduced price of the book=Rs.(x - 5)
? Number of books bought for Rs.200 = 200/(x - 5)
Now, according to the condition,
200/(x - 5) - 200/x = 2
? (200x - 200x + 1000)/(x - 5)x = 2
? (200x - 200x + 1000)/x(x - 5) = 2
? 1000/x(x - 5) = 2
? 1000/x(x - 5) = 1
? 1000/x(x - 5) = 2
? 500/x(x - 5) = 1
? 500 = x(x-5)
? x2 -5x - 50 = 0
? x2- 25 + 20x - 500 = 0
? x(x - 25) + 20(x - 25) = 0
? (x - 25)(x + 20) = 0
? x - 25 = 0 or x + 20 = 0
? x = 25 0r -20
? x = 25 (since,x cannot be negatives)
So, the original price of the bok is Rs.25.
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 .....(i)
When 10 more gold coins are added, then total number of gold coins becomes x + 10 and the number of non-gold coins remain the same as y.
Now,we have 2(10 + x) = y ....(ii)
On 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.
Correct Answer: 25 and 25
Explanation:
Total number of coins = 50
Let ? 1 coins = x and ? 2 coins = y
Now,according to the question,
x + y = 50 ... (i)
and x + 2y = 75 ...(ii)
On solving Eqs.(i) and (ii),we get
x = 25 and y = 25
Correct Answer: 45
Explanation:
Let the number of correct answers marked be c and the number of wrong answers marked be w.
According to the question,
c + w = 60 ...(i)
Also, 3c - w = 120 ...(ii)
On adding Eqs.(i) and (ii), we get c = 45
So, the questions marked correct are 45.
Correct Answer: 83
Explanation:
Let the digit in the unit's place be y and digit in the ten's place be x.
? Number = 10x + y
Then, x = 2y + 2
? x - 2y - 2 = 0 ...(i)
Number obtained by reversing the digits = 10y + x
Then, 10y + x = 5 + 3(x + y)
? 2x - 7y + 5 = 0 ...(ii)
On multiplying Eq.(i) by 2 and then subtracting it from Eq. (ii), we get y = 3
On substituting the value of y in Eq.(i), we get x = 8
So, the two-digit number is 83.
Correct Answer: 4
Explanation:
x3 + 1 + 2x = 6x + 1/x
x3 + 1 + 2x = (6x2 + 1) / x
(x3 + 1 + 2x)x = 6x22 + 1
x4 + x + 2x2 - 6x2 - 1 = 0
x4 - 4x2 + x - 1 = 0
Degree of polynomial is highest exponent degree term i. e., 4.
Correct Answer: ? 12
Explanation:
Let the length of the piece be L m.
Then,rate per metre = ? 120/L
New length = (L + 2) m
Since, the cost remains same.
? New rate per metre =Rs.120/(L + 2)
According to the given condition, 120/L - 120/(L + 2) = 2
? [120(L + 2) - 120L]/L(L + 2) = 2
? [120L + 240 - 120L] / L(L + 2) = 2
? [120L + 240 -120L] / L(L + 2) = 2
? 240/L(L + 2) = 2
? 240 = 2L(L + 2)
? 120 = L(L + 2) = L2 + 2L
? L2 + 2L - 120 = 0
? L2 + 12L - 10L - 120 = 0
? L(L + 12) - 10 x (L + 12) = 0
? (L + 12)(L - 10) = 0
? L + 12 = 0 or L - 10 = 0
? L = -12 or 10
? L = 10(since, L cannot be negative)
? Original rate per metre of cloth = 120/L = 120/10 = ? 12
Correct Answer: 0.9
Explanation:
Correct Answer: 3 sq. units
Explanation:
Correct Answer: 12
Explanation:
According to question , we have
?( x - 0 )2 + ( 0 + 5 )2 = 13
? x2 + 25 = 169
? x2 = 169 - 25 = 144
? x = ?144 = 12
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