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Every year Aman consumes 250 kg wheat and 90 kg rice. The price of wheat is 20% of the price of rice and he spends a total of Rs. 3500 on wheat and rice per year. If the price of rice is increased by 20% then what is the percentage reduction of wheat consumption for the same expenditure of Rs. 3500? (Given that the price of wheat and consumption of rice is constant)


Options:
A .   24%
B .   40%
C .   25%
D .   36%
Answer: Option D
:
D

Let the price of Wheat =X per kg. Then, the price of Rice =5X per kg (As it is given that the price of Wheat is 20% the price of Rice.)
 Wheat                                           Rice
  250                                               90
x250 x                                             5x450 x
700 X = 3500
X=5
Hence the price of wheat is = Rs.5 per kg
Let the new amount of wheat be M kg,then M×5+90×30=3500;M=160
(As the price of Rice increases by 20%  i.e., from Rs.25 to Rs.30)
Hence decrease (in %) of amount of wheat =250160250×100=36%
Alternate Method:
As wheat is 20% of rice, instead of consuming 250 kg of wheat, Aman can consume 50 kg of rice. Hence,
(50+90)x=3500     X=25.
Now,x(25)+90(30)=3500. x=32.
Therefore,change in consumption =50 - 32=18kg.
Thus,percentage increase will be 1850  or 36%



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