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Kate has some oranges with her. She eats half of her oranges every day. After eating the oranges, she is given four more oranges. After 3 days, she is left with 32 oranges. How many oranges she had in beginning?

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Kate has some oranges with her. She eats half of her oranges every day. After eating the oranges, she is given four more oranges. After 3 days, she is left with 32 oranges. How many oranges she had in beginning?


1). 130
2). 160
3). 150
4). 100


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Answered by on | Votes 0 |

Suppose Kate has T oranges in beginning.

She eats half of her oranges and then gets 4 more oranges daily.

If she has N oranges on a day, she will have [(N/2) + 4] at end of day.

Number of oranges after 1 day = (T/2) + 4 = 0.5T + 4

Number of oranges after 2 days = ((0.5T + 4)/2) + 4

= 0.25T + 6

Number of oranges after 3 days = ((0.25T + 6)/2 ) + 4

= 0.125T + 7

This should be equal to 32.

⇒ 0.125T + 7 = 32

⇒ T = 25/0.125 = 200

∴ Kate had 200 oranges in beginning.

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