Question

If 2 kg of almonds costs as much as 8 kg of walnuts and the cost of 5 kg of almonds and 16 kg of walnuts is Rs 1080. The cost of almonds per kg is.
a. Rs. 160
b. Rs. 150
c. Rs. 120
d. Rs. 140

Answer 1

Hint: In order to solve this question, we will consider the cost of 1 kg almonds as x and the cost of 1 kg walnuts as y and then we will form 2 linear equations of 2 variables then we will apply the substitution method to find the cost of almonds, that is, x.

Complete step-by-step answer:
In this question, we have been asked to find the cost of almonds when it is given that 2 kg of almonds cost as much as 8 kg of walnuts and the cost of 5 kg of almonds and 16 kg of walnuts is Rs 1080.
To solve this question, let us consider the cost of 1 kg almonds as Rs. x and the cost of 1 kg walnuts as Rs. y. So, according to the conditions given in the question, we can write,
2x = 8y ……… (i)
We have also been given that the cost of 5 kg of almonds and 16 kg of walnuts is Rs 1080. So, we can write it as,
5x + 16y = 1080 ……… (ii)
Now, from equation (i), we get $y=\dfrac{1}{4}x$ so, we will put this value of y in equation (ii). So, we will get,
$5x+16\times \dfrac{1}{4}x=1080$
Now, we will simplify it further to get the answer.
5x + 4x = 1080
Now, we know that like term add, so we get,
9x = 1080
Now, we will divide the whole equation by 9, so we get,
$x=\dfrac{1080}{9}=120$
Hence, we can say that the cost price of 1 kg almonds is Rs. 120. Therefore option (c) is the correct answer.

Note: We can also find the value of y first and then we can find the value of x by using the value of y. But that will increase the number of steps and there will be chances of calculation mistakes also. So, it is better to directly find the value of x. Also, we can find the value of x by elimination method.