Let a fruit bowl contain $x$ number of fruits. After some time, Kavya adds one more than the initial number of fruits to the same bowl. If Shravya takes out two fruits from the same bowl, then the number of fruits remaining in the bowl is

$2 x - 2$

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$x - 1$

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$x - 2$

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$2 x - 1$

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Solution

The correct option is D
$2 x - 1$

The initial number of fruits in the fruit bowl = $x$

Kavya adds one more than the initial number of fruits to the same bowl. i.e., Kavya adds $x + 1$ number of fruits.

Then the total number of fruits in the bowl now = $x + (x + 1)$

We know that if we take any natural number and add the next natural number, or if we double the first number and add 1, we get the same number as the result.

Then $x + (x + 1) = 2 x + 1$

Therefore the total number of fruits in the bowl after Kavya adds one more than the initial number of fruits = $x + (x + 1) = 2 x + 1$

Given, Shravya takes out two fruits from the same bowl.

Then the total number of fruits after Shravya takes out two fruits from the bowl = $(2 x + 1) - 2$

But then $(2 x + 1) - 2 = (2 x + 1) - 1 - 1 = [(2 x + 1) - 1] - 1$

We know that $(x + y) - y = x$ , for all numbers $x, y$ .

So, $(2 x + 1) - 2 = [(2 x + 1) - 1] - 1 = [2 x] - 1 = 2 x - 1$

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Let a fruit bowl contain x number of fruits. After some time, Kavya adds one more than the initial number of fruits to the same bowl. If Shravya takes out two fruits from the same bowl, then the number of fruits remaining in the bowl is

Let a fruit bowl contain $x$ number of fruits. After some time, Kavya adds one more than the initial number of fruits to the same bowl. If Shravya takes out two fruits from the same bowl, then the number of fruits remaining in the bowl is