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Q.

The cost of 5 oranges and 3 apples is Rs. 35 and the cost of 2 oranges and 4 apples is Rs. 28. Find the cost of an orange and an apple.


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a

Orange=Rs. 4, Apple =Rs. 5

b

Orange=Rs. 4, Apple =Rs. 4

c

Orange=Rs. 3, Apple =Rs. 5

d

Orange=Rs. 4, Apple =Rs. 3 

answer is A.

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Detailed Solution

Given that, the cost of 5 oranges and 3 apples is Rs 35.
Let cost of an orange be Rs. x and cost of an apple be Rs. y.
Then,
5x+3y=35        … (1)
Also, the cost of 2 oranges and 4 apples is Rs28 then,
2x+4y=28 ⇒2(x+2y)=28 ⇒2(x+2y)=28 ⇒x+2y=14        … (2)
The conventional version of the aforementioned equations (1) and (2) is as follows:
  5x + 3y − 35 = 0 ……. 3 x + 2y  14 = 0 ……. 4  
On comparing equation (3) and (4) with the standard form
  a 1 x+ b 1 y+ c 1 =0  and a 2 x+ b 2 y+ c 2 =0  :
we get,
  a 1 = 5,   b 1 = 3 and   c 1 = −35 a 2 = 1,  b 2 =2 and   c 2 =−14  
 Then,
  a 1 a 2 =  5 1   ,    b 1 b 2  = 3 2 ,   c 1 c 2  =  −35 −14 ∵ a 1 a 2 ≠ b 1 b 2 ≠ c 1 c 2  
Therefore, using the cross-multiplication approach
Question ImageThen,
Question Image x 3×−14 − 2×−35  =  y −35×1 − −14×5  =  1 5×2 − 1×3   x - 42 + 70   =  y −35+70  =  1 10−3   x 28   =  y 35  =  1  7  
   I        II      III    Taking terms, I and III:
  x 28 =  1 7 x= 28 7 x=4  
Taking terms II and III:
  y 35  =  1  7 y= 35 7 y=5  
⇒The cost of an orange is Rs.4 and cost of an apple is Rs.5.
Hence, option (1) is correct.
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