A group of students decided to buy a Alarm Clock priced between Rs. 170 to Rs 195. But at the last moment, two students backed out of the decision so that the remaining students had to pay 1 Rupee mor

Question

A group of students decided to buy a Alarm Clock priced between Rs. 170 to Rs 195. But at the last moment, two students backed out of the decision so that the remaining students had to pay 1 Rupee more than they had planned. If the students paid equal shares, the price of the Alarm Clock is

TestHub · Accepted Answer

Let x be the price, n the initial number of students. n − 2 x ​ = n x ​ + 1 ⇒ x = 2 n ( n − 2 ) ​ . Given 170 ≤ x ≤ 195 . 340 ≤ n 2 − 2 n ≤ 390 . For n = 19 , 1 9 2 − 2 ( 19 ) = 361 − 38 = 323 . For n = 20 , 2 0 2 − 2 ( 20 ) = 400 − 40 = 360 . For n = 21 , 2 1 2 − 2 ( 21 ) = 441 − 42 = 399 . So n = 20 is the only integer solution. The final answer is 180 ​ .

Mathematics - Quadratic Equation Question with Solution | TestHub

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