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- Question
- A man covers a distance of 18 km in 5 h party by walking and partly by running. if he walks at 2 km/h and runs at 6km/h, then find the distance he covers by running?
Options- A. 12 km
- B. 15 km
- C. 10 km
- D. 9 km
- Correct Answer
- 12 km
ExplanationLet the distance covered by walking be x km.
Speed while walking = 2 km/h
Time spent on walking = x/2 h
Now, distance covered by runnig = (18 - x) km
Speed while running = 6 km/h
Time spent on running = (18 - x)/6 h
?x/2 + (18 -x)/6 = 5
? (3x + 18x - x)/6 = 5
? 2x + 18 = 30
? 2x = 12
? x = 6
? The distance covered by running = 18 - 6 = 12 km - 1. A student was asked to find 2/5th of a number and he instead multiplied it by 5/2. As a result he got an answer which was more than the correct answer by 5208. What was the number?
Options- A. 2485
- B. 2456
- C. 2480
- D. 2455 Discuss
- 2. If the polynomials ax 3 + 4x 2 -3x - 4 and x 3 - 4x + a leave the same remainder when divided by (x - 3). Then, what is the value of a?
Options- A. 2
- B. -1
- C. 3
- D. 4 Discuss
- 3. Find the remainder when f(x) = x 4 - 6x 3 + 2x 2 + 3x + 1 is divided by (x - 2)?
Options- A. -12
- B. 12
- C. 17
- D. -17 Discuss
- 4. A sum of Rs. 13.50 is made by 38 coins which are either 50 paise or 25 paise. Find the number of 25 paise coins?
Options- A. 16
- B. 24
- C. 18
- D. 22 Discuss
- 5. 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 = 0 Discuss
- 6. Ramesh and Ganesh had some oranges initially. If Ramesh gave 5 oranges to Ganesh, then Ganesh will have thrice as many oranges as Ramesh. Instead of that, if Ganesh was to give 5 oranges to Ramesh, then they both will have the same number of oranges. Find the ratio of oranges that were distributed between Ramesh and Ganesh?
Options- A. 3 : 5
- B. 1 : 3
- C. 5 : 7
- D. 7 : 9 Discuss
- 7. 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
- 8. 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
- 9. 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
- 10. 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
Elementary Algebra problems
Search Results
Correct Answer: 2480
Explanation:
Let the number be x. Then,
5x/2 - 2x/5 = 5208
? (25x - 4x)/10 = 5208
? 21x/10 = 5208
? 21x = 5208 x 10
? x = (5208 x 10)/21
? x = 2480
So, the original numbers was 2480.
Correct Answer: -1
Explanation:
Since, p(x) = ax3 + 4x2 + 3x - 4 and q(x) = x3 -4x + a divided by x - 3, hence p(3) = q(3)
? a x 33 + 4 x 32 + 3 x 3 - 4 = 33 - 4 x 3 + a
? a = -1
Correct Answer: -17
Explanation:
When f(x) = x4 - 6x3 + 2x2 + 3x + 1 is divided by (x - 2), then remainder can be calculated by putting x - 2 = 0
i.e. x = 2
Now, put x = 2 in f(x)
f(2) = (2)4 - 6(2)3 + 2(2)2 + 3 x 2 + 1
= 16 - 48 + 8 + 6 + 1 = -17
? The remainder will be - 17.
Correct Answer: 22
Explanation:
Let the number of 25 paise coins and 50 paise cons be x and y,respectively.
According to the question,
x + y = 38
Also, 25x + 50y = 1350
On multiplying Eq.(i) by 25 and substracting from Eq.(ii), we get y =16
On substituting the value of y in Eq.(i),we get y=22
So,the number of 25 paise coins in 22.
Correct Answer: y = 4x
Explanation:
The linear equation is y = 4x,
When, x = 1, y = 4
Correct Answer: 3 : 5
Explanation:
Let the number of oranges Ramesh has be x and the number of oranges Ganesh has be y.
According to the first condition,
y + 5 = 3(x - 5)
? 3x - y + 10 = 0 ...(i)
According to the second condition,
x + 5 = y - 5
? x - y + 10 = 0 ...(ii)
On subtracting Eq. (ii) from Eq. (i), we get x = 15
On substituting the value of x in Eq.(ii), we get y = 25
? The ratio of oranges to be distributed Ramesh and Ganesh = 15:25 = 3:5
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: 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: 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: 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.
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