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A man bought certain number of toys for rs 180 .he kept one for his own and sold rest for one rs each more than he gave for them besides getting his own toy for nothing he made a profit of rs 10 .find the no of boys?
Verified Answer
A man bought certain number of toys for rs 180 .he kept one for his ow...
Let man bought n toys
Then, cost of one toy = Rs 180 / n
He kept one toy for his own.
According to question
After selling (n – 1) toys, he made a profit of Rs 10 by selling each toy for Rs (180 / n) + 1
so that
⇒ ( n – 1)( (180 / n )+ 1 ) = 180 + 10.
⇒ (n – 1)( 180 / n) + ( n – 1) = 190
⇒ 180 - ( 180 / n) + n – 1 = 190
⇒ n2 – 11n - 180 = 0
⇒ n2 – 20n + 9n - 180 = 0
⇒ n(n – 20) + 9(n - 20) = 0
⇒ (n + 9)(n - 20) = 0
n = -9 or 20 ( the number of toys never be negative))
∴ the man has bought 20 toys.
This question is part of UPSC exam. View all Class 10 courses
Most Upvoted Answer
A man bought certain number of toys for rs 180 .he kept one for his ow...
Problem:
A man bought a certain number of toys for Rs 180. He kept one toy for himself and sold the rest for Rs 1 each more than what he paid for them. Besides getting his own toy for nothing, he made a profit of Rs 10. Find the number of toys he bought.
Solution:
Let's assume the number of toys the man bought is 'x'.
Cost of x toys:
The total cost of 'x' toys is Rs 180.
Cost of one toy:
The cost of one toy would be Rs 180 divided by 'x'.
Selling price of one toy:
The man sold the remaining (x-1) toys for Rs 1 each more than the cost price of one toy. Therefore, the selling price of one toy would be (cost price + Rs 1).
Profit:
The man made a profit of Rs 10. This means the selling price of (x-1) toys was Rs 10 more than the cost price of (x-1) toys.
Equation 1:
We can write the equation for the total cost of the toys as:
Total cost = Cost of one toy * Number of toys
180 = (180/x) * x
Equation 2:
We can write the equation for the profit as:
Profit = Selling price of (x-1) toys - Cost price of (x-1) toys
10 = [(180/x) + 1] * (x - 1)
Simplifying Equation 1:
180 = 180
This equation is true for any value of 'x' as both sides are equal.
Simplifying Equation 2:
10 = [(180/x) + 1] * (x - 1)
10 = (180/x + x - 1)
10 = (180 + x^2 - x) / x
10x = 180 + x^2 - x
x^2 - x - 10x + 180 = 0
x^2 - 11x + 180 = 0
Factorizing the quadratic equation:
(x - 9)(x - 20) = 0
Roots of the equation:
x = 9 or x = 20
Conclusion:
The man could have bought either 9 toys or 20 toys.
A man bought a certain number of toys for Rs 180. He kept one toy for himself and sold the rest for Rs 1 each more than what he paid for them. Besides getting his own toy for nothing, he made a profit of Rs 10. Find the number of toys he bought.
Solution:
Let's assume the number of toys the man bought is 'x'.
Cost of x toys:
The total cost of 'x' toys is Rs 180.
Cost of one toy:
The cost of one toy would be Rs 180 divided by 'x'.
Selling price of one toy:
The man sold the remaining (x-1) toys for Rs 1 each more than the cost price of one toy. Therefore, the selling price of one toy would be (cost price + Rs 1).
Profit:
The man made a profit of Rs 10. This means the selling price of (x-1) toys was Rs 10 more than the cost price of (x-1) toys.
Equation 1:
We can write the equation for the total cost of the toys as:
Total cost = Cost of one toy * Number of toys
180 = (180/x) * x
Equation 2:
We can write the equation for the profit as:
Profit = Selling price of (x-1) toys - Cost price of (x-1) toys
10 = [(180/x) + 1] * (x - 1)
Simplifying Equation 1:
180 = 180
This equation is true for any value of 'x' as both sides are equal.
Simplifying Equation 2:
10 = [(180/x) + 1] * (x - 1)
10 = (180/x + x - 1)
10 = (180 + x^2 - x) / x
10x = 180 + x^2 - x
x^2 - x - 10x + 180 = 0
x^2 - 11x + 180 = 0
Factorizing the quadratic equation:
(x - 9)(x - 20) = 0
Roots of the equation:
x = 9 or x = 20
Conclusion:
The man could have bought either 9 toys or 20 toys.
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A man bought certain number of toys for rs 180 .he kept one for his own and sold rest for one rs each more than he gave for them besides getting his own toy for nothing he made a profit of rs 10 .find the no of boys?
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A man bought certain number of toys for rs 180 .he kept one for his own and sold rest for one rs each more than he gave for them besides getting his own toy for nothing he made a profit of rs 10 .find the no of boys? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A man bought certain number of toys for rs 180 .he kept one for his own and sold rest for one rs each more than he gave for them besides getting his own toy for nothing he made a profit of rs 10 .find the no of boys? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man bought certain number of toys for rs 180 .he kept one for his own and sold rest for one rs each more than he gave for them besides getting his own toy for nothing he made a profit of rs 10 .find the no of boys?.
A man bought certain number of toys for rs 180 .he kept one for his own and sold rest for one rs each more than he gave for them besides getting his own toy for nothing he made a profit of rs 10 .find the no of boys? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A man bought certain number of toys for rs 180 .he kept one for his own and sold rest for one rs each more than he gave for them besides getting his own toy for nothing he made a profit of rs 10 .find the no of boys? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man bought certain number of toys for rs 180 .he kept one for his own and sold rest for one rs each more than he gave for them besides getting his own toy for nothing he made a profit of rs 10 .find the no of boys?.
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