Question

Two kg of pears and 3 kg of apples together cost ₹ 4.26 whereas 3 kg of pears and 2 kg of apples cost ₹ 4.49. How much does apple cost per kg?
(A) 0.32
(B) 0.52
(C) 0.99
(D) 0.76

Answer 1

Hint:Assign two variables to the cost of 1 kg of apple and pear respectively. Then formulate two linear equations using the information about cost given in the question. Solve the linear equations to get the values of the variables. That would be your answer.

Complete step-by-step Solution:
Let the cost of 1kg of pear is $x$ and the cost of 1kg of apple is $y$
Then, the first part of the question can be simplified as
$\Rightarrow 2x + 3y = 4.26$ . . . (1)
And the second part of the equation can be simplified as
$\Rightarrow 3x + 2y = 4.49$ . . . (2)
Multiplying equation (1) by 3, we get
$\Rightarrow 6x + 9y = 12.78$ . . . . . . (3)
And multiplying equation (2) by 2, we get
$\Rightarrow 6x + 4y = 8.98$ . . . . . (4)
Subtract the equation (4) from equation (3), we get
\[5y = 3.8\]
$ \Rightarrow y = \dfrac{{3.8}}{5}$
$ \Rightarrow y = 0.76$
Hence, 1kg of apple cost ₹ 0.76

Therefore, from the above explanation, the correct answer is, option (D) $0.76$

Additional information:
If we were to find the cost of 1kg of pear as well, then we could do that but substituting the value of $y$in any of the equations above. Let us put the value of $y$in equation (1)
Then, we get
$2x + 3 \times 0.76 = 4.26$
$ \Rightarrow 2x + 2.28 = 4.26$
rearranging the above equation, we get
$2x = 4.26 - 2.28$
$ \Rightarrow 2x = 1.98$
$ \Rightarrow x = \dfrac{{1.98}}{2}$
$ \Rightarrow x = 0.99$

Hence, the cost of 1kg of pear is ₹ 0.99

Note:While rounding off it is the dividend that is being rounded off because the divisor already has only $1$ significant digit so it cannot be further rounded off to $2$, since $2$ being smaller than $5$, will otherwise make the denominator $0$ and the division will become invalid, since anything divided by $0$ is not defined.