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11 Feb 2020, 01:41
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Adam, Eve, Eva and Aram were supposed to work on a college competition, in which their ratio of the time spent by each of them was in the ratio 1: 2: 3: 4 respectively. The prize money was supposed to be split between them in the ratio of the time devoted to the competition. But Aram left before the work even started and the time spent by the rest of them remained unchanged. The prize money was split between the rest of the three and Eva received $50 extra than she was supposed to receive. Which of the following could be prize money?
A) 150
B) 200
C) 250
D) 400
E) 450
A) 150
B) 200
C) 250
D) 400
E) 450
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11 Feb 2020, 02:16
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Time ratio of Adam: Eve: Eva: Aram = 1: 2: 3: 4,
Time ratio of Adam: Eve: Eva = 1: 2: 3
Extra amount received by Eva = $50
Let the actual prize money be $P.
Since the ratio of Adam: Eve: Eva: Aram = 1: 2: 3: 4
Amount that Eva gets = 3×p/10=3P/10
After Aram, the money is split between the rest of the three, in the ratio = 1: 2: 3
Amount that Eva receives = 3×p/6=P/2
Extra amount that Eva receives = P/2−3P/10=2P/10=P/5
As per the given question, we know that this P/5 = $50
So, P = $250
Time ratio of Adam: Eve: Eva = 1: 2: 3
Extra amount received by Eva = $50
Let the actual prize money be $P.
Since the ratio of Adam: Eve: Eva: Aram = 1: 2: 3: 4
Amount that Eva gets = 3×p/10=3P/10
After Aram, the money is split between the rest of the three, in the ratio = 1: 2: 3
Amount that Eva receives = 3×p/6=P/2
Extra amount that Eva receives = P/2−3P/10=2P/10=P/5
As per the given question, we know that this P/5 = $50
So, P = $250
