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Q.

A sum of Rs. 2800 is to be used to award four prizes. If each prize after the first is Rs. 200 less than the preceding prize, then what is the value of each of the prizes?


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a

Rs.1000,Rs.800,Rs.600, and Rs.400

b

Rs.1500,Rs.400,Rs.500, and Rs.200

c

Rs.2000,Rs.700,Rs.500, and Rs.300

d

Rs.1100,Rs.900,Rs.650, and Rs.450  

answer is B.

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Detailed Solution

Given that each prize after the first Rs. 200 is less than the preceding prize.
Let the amount of the first prize is Rs. ‘a’.
Therefore, the amounts of the four prizes are in A.P.
So, according to given condition amount of the second prize = Rs(a - 200).
Amount of the third prize = Rs (a - 400)
Amount of the fourth prize = Rs (a - 600)
Total sum of four prizes = Rs. 2800
∴a+(a−200)+(a−400)+(a−600)=2800 ⇒4a−1200=2800 ⇒4a=4000 ⇒a=1000
Thus, amount of the first prize Rs. 1000.
Then amount of the second prize is,
=Rs⋅(1000−200) =Rs.800
 Now amount of the third prize is,
=Rs⋅(1000−400) =Rs.600 Then amount of the fourth prize is,
=Rs⋅(1000−600) =Rs.400
Therefore, the value of each of the prize is Rs.1000,Rs.800,Rs.600, and Rs.400 .
Hence, option (2) is correct.
 
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