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A tourist has ₹ 10,000 with him. He calculated that he could spend ₹ x everyday on his holidays. He spent $x − 50$ everyday and extended his holidays by 10 days. Calculate x.

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100

300

150

250

answer is C.

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Detailed Solution

Let x be the amount of money he spent each day, y be the number of days he spent.
So,

x y = 10000

…..(1)
He spends ₹ (x-50) everyday, the no. of days he spends the same amount is

(y + 10)

. So according to question,

\Rightarrow (x - 50) (y + 10) = 10000

\Rightarrow xy + 10 x - 50 y - 500 = 10000

Substitute xy=10000

\Rightarrow 10000 + 10 x - 50 y - 500 = 10000

\Rightarrow 10 x - 50 y - 500 = 0

Dividing the above equation by 10,

⇒ x − 5 y − 50 = 0 ⇒ x = 5 y + 50.... (2)

Substituting

x

in 1

\Rightarrow (5 y + 50) y = 10000

\Rightarrow 5 y^{2} + 50 y = 10000

\Rightarrow y^{2} + 10 y - 2000 = 0

\Rightarrow y^{2} + 50 y - 40 y - 2000 = 0

\Rightarrow y (y + 50) y - 40 (y + 50) = 0

\Rightarrow (y - 40) (y + 50) = 0

\Rightarrow y = 40, y = - 50

y is number of days spent so it cannot be negative.
When y=40, the value of x is,

⇒ x y = 10000 ⇒ x = 1000040 ⇒ x = 250

Hence, the value of x is 250.
Therefore, the correct option is 3.

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