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There are $$3$$ pineapples, $$6$$ bananas and $$7$$ apples. Each fruit of the same category has the same price. The total amount of the fruits in the first row is Rs. $$44$$, that of the third row is Rs. $$54$$ and that of the first column is Rs. $$72$$. Then the total amount in rupees of the fruits in the second row is
Correct Answer: 82
Let the cost of one apple be $$a$$, one banana be $$b$$, and one pineapple be $$p$$.
From the first row,
$$a+b=22.$$
From the third row,
$$p+a+2b=54.$$
From the first column,
$$2a+p+b=72.$$
From the first equation,
$$a=22-b.$$
Substitute this into the second equation.
$$p+(22-b)+2b=54.$$
$$p+b=32.$$
So,
$$p=32-b.$$
Now substitute $$a=22-b$$ and $$p=32-b$$ into the third equation.
$$2(22-b)+(32-b)+b=72.$$
$$44-2b+32-b+b=72.$$
$$76-2b=72.$$
$$2b=4.$$
$$b=2.$$
Now,
$$a=22-2=20,$$
and
$$p=32-2=30.$$
The cost of the second row is
$$a+2p+b=20+2(30)+2=82.$$
Hence, the cost of the second row isΒ $$82$$
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