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ICSE Class 10 Answered

The hotel bill for a no.of people for overnight stay is Rs: 4800 if there were 4 more , the bill each person had to pay would hv reduced by rs 200 . Find the no.of people staying overnight
Asked by chaitanyachaitanyanani | 04 Feb, 2019, 04:27: PM
answered-by-expert Expert Answer
 
begin mathsize 16px style Let space the space number space of space people space staying space overnight space be space straight x.
According space to space the space condition space in space the space question comma space we space get
4800 over straight x minus fraction numerator 4800 over denominator straight x plus space 4 end fraction equals space 200
rightwards double arrow 4800 space open parentheses 1 over straight x minus fraction numerator 1 over denominator straight x space plus space 4 end fraction close parentheses space equals space 200
rightwards double arrow fraction numerator straight x space space plus space space 4 space minus space straight x over denominator straight x squared plus space 4 straight x end fraction space equals space 1 over 24
rightwards double arrow straight x squared plus space 4 straight x space minus space 96 space equals space 0
Here space straight a space equals space 1 comma space straight b space equals space 4 space and space straight c space equals space minus space 96
straight D space space equals space straight b squared space minus space 4 ac space equals space open parentheses 4 close parentheses squared space minus space 4 space cross times space 1 space cross times space minus 96 equals 16 space plus 384 space equals space 400
rightwards double arrow straight x space space space equals space space space fraction numerator negative straight b plus-or-minus square root of straight D over denominator 2 straight a end fraction space equals space fraction numerator negative 4 plus-or-minus square root of 400 over denominator 2 cross times 1 end fraction equals fraction numerator negative 4 plus-or-minus 20 over denominator 2 end fraction
rightwards double arrow straight x space equals space fraction numerator negative 24 over denominator 2 end fraction space equals space minus 12 space or space straight x space equals space 16 over 2 space equals 8
No space of space people space can apostrophe straight t space be space negative.
rightwards double arrow straight x space equals space 8
Therefore space the space number space of space people space staying space overnight space is space 8. end style
Answered by Yasmeen Khan | 05 Feb, 2019, 02:08: PM
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