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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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Orange

= Rs . 4

, Apple

= Rs . 5

Orange

= Rs . 4

, Apple

= Rs . 4

Orange

= Rs . 3

, Apple

= Rs . 5

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,

5 x + 3 y = 35

… (1)
Also, the cost of 2 oranges and 4 apples is Rs28 then,

2 x + 4 y = 28

\Rightarrow 2 (x + 2 y) = 28

\Rightarrow 2 (x + 2 y) = 28

\Rightarrow x + 2 y = 14

… (2)
The conventional version of the aforementioned equations (1) and (2) is as follows:

5 x + 3 y − 35 = 0 … … . 3 x + 2 y 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 a n d c 1 = − 35 a 2 = 1, b 2 = 2 a n d c 2 = − 14

Then,

a 1 a 2 = 51, b 1 b 2 = 32, 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 Image

Then,

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 = 17

I        II      III

Taking terms, I and III:

x 28 = 17 x = 287 x = 4

Taking terms II and III:

y 35 = 17 y = 357 y = 5

\Rightarrow

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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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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