Elementary Algebra
- 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 ?
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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 = 1350Correct Option: D
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.
- 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 ?
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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 = 60Correct Option: A
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.
- 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 ?
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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)Correct Option: D
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
- 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 ?
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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)
Correct Option: A
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.
- 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 ?
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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)Correct Option: A
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.
