A man bought certain number of chairs for rs 10000. he kept one for his own use and sold the rest at the rate rs 50 more than he gave for one chair. beside getting his own chair for nothing he made a profit of rs 450. hiw many chairs he buy?
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n = number of chairs purchased
p = price paid per chair
np = 10,000 so p=10,000/n
(n-1)(p+50)=10450
np+50n-p-50=10450
10000+50n-(10000/n)-50=10450
Subtract 10,000 from both sides and add 50 to both sides. Add 50n and 10,000/n by using n as the common denominator.
(50n^2 - 10000)/n = 500
50n^2 - 10000 = 500n
50n^2 - 500n - 10000 =0
n^2 - 10n - 200 = 0
(n-20)(n+10)=0
n=20 and n=-10
Can't use -10 because there can't be a negative number of chairs. The answer is 20.
p = price paid per chair
np = 10,000 so p=10,000/n
(n-1)(p+50)=10450
np+50n-p-50=10450
10000+50n-(10000/n)-50=10450
Subtract 10,000 from both sides and add 50 to both sides. Add 50n and 10,000/n by using n as the common denominator.
(50n^2 - 10000)/n = 500
50n^2 - 10000 = 500n
50n^2 - 500n - 10000 =0
n^2 - 10n - 200 = 0
(n-20)(n+10)=0
n=20 and n=-10
Can't use -10 because there can't be a negative number of chairs. The answer is 20.
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