Discussion

Question:

A group of students decided to buy speakers for a party worth Rs. 600. But at the last moment, five students backed out, so each of the remaining had to pay Rs. x more than what they had planned. If ten students had backed out, each of the remaining would have had to pay Rs. 10 more than what they had planned. Find the value of x and total number of students.

Explanation:

Let the total number of students be 'n'.

Cost of the speaker = Rs. 600

Let the price to be paid by each student initially be 'y'.

So, n × y = 600   …(1)

Now, five students backed out, and average price increased by 'x' i.e.

⇒ (n - 5) × (y + x) = 600   …(2)

Now, if ten students had backed out, average price would have increased by Rs. 10 i.e.

⇒ (n - 10) × (y + 10) = 600   …(3)

Solving the three equations:

From (1) and (3):

$\left(\frac{600}{y}-10\right)\left(y+10\right)$ = 600

y² + 10y – 600 = 0

y = $\frac{-10\pm \sqrt{100+2400}}{2}$ = 20

⇒ y = 20

⇒ n = 600/20 = 30 (# students)

∴ x = 600/(30 - 5) - 20 = 4 [From (2)]

x = 4

Hence, option (b).

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