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Quantitative Reasoning – Practice – Calculate the the number of benches!

quadratic equation onlinepsa_in

PSA_LEVEL-UP_QNR15. There are 600 people to be seated, but there are 10 benches less. If two more people are asked to seat on each bench, then everybody is accomodated. How many benches were there?

A) 40
B) 10
C) 50
D) Cannot be determined.

Ans: Let there are ‘b’ benches and every bench can accommodate ‘r’ people.

According to the question.

(b+10)*r=600 [“If 10 benches were added” case]
Also, (b)* (r+2) = 600 [“If every bench has two more” case]

Thus, br + 10r = br + 2b
=>r:b =1:5.

b= 5r. Substituting in one of the equation

5r^2 + 10r -600 = 0      [Quadratic equation]

r^2 + 2r -120 = 0

r^2 + 12r -10r -120 = 0

r(r + 12)  -10 (r +12) = 0
r= 10; -12 [-ve is rejected].

Now, b=5r =50.

Number of benches = 50.

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