Question

The total cost of $8$ buckets and $5$ mugs is $Rs.92$ and the total cost of $5$ buckets and $8$ mugs is $Rs.77$. Find the cost of $2$ mugs and $3$ buckets.

Answer 1

Hint: We can let each variable for the cost per unit for bucket and mug. Then we get two equations using the given information. Solving it we get the unit costs. Thus we can find the required cost.

Complete step-by-step answer:
It is given that the total cost of $8$ buckets and $5$ mugs is $Rs.92$ and the total cost of $5$ buckets and $8$ mugs is $Rs.77$.
We are asked to find the cost of $2$ mugs and $3$ buckets.
Let the cost of a bucket be $x$ and a mug be $y$.
This gives the cost of $8$ buckets as $8x$ and cost of $5$ mugs as $5y$.
So the total cost of $8$ buckets and $5$ mugs is $8x + 5y$.
It is given that this cost is equal to $Rs.92$.
So we can write $8x + 5y = 92 - - - (i)$
Similarly we have, total cost of $5$ buckets and $8$ mugs is $5x + 8y$.
It is given that this cost is equal to $Rs.77$.
So we have, $5x + 8y = 77 - - - (ii)$
To find the value of $x$ and $y$ we have to solve the two equations.
To eliminate one of the variables, make the coefficient of any of the variables be same.
For, multiply equation $(i)$ by $5$ and equation $(ii)$ by $8$.
This gives,
$40x + 25y = 460 - - - (iii)$
$40x + 64y = 616 - - - (iv)$
Subtracting equation $(iii)$ from equation $(iv)$ we get,
$39y = 156$
Dividing both sides by $39$ we get,
$y = \dfrac{{156}}{{39}} = 4$
Substitute the value of $y$ in equation $(i)$ we get,
$8x + 5 \times 4 = 92$
$ \Rightarrow 8x + 20 = 92$
Subtracting $20$ from both sides we get,
$ \Rightarrow 8x = 92 - 20 = 72$
Dividing both sides by $8$ we get,
$x = \dfrac{{72}}{8} = 9$
So we have, $x = 9,y = 4$
That is, the cost of a bucket is $Rs.9$ and cost of a mug is $Rs.4$.
We are asked the cost of $2$ mugs and $3$ buckets, which is equal to $2y + 3x$.
Substituting we get,
Cost of $2$ mugs and $3$ buckets, $C = 2 \times 4 + 3 \times 9 = 8 + 27 = 35$
Therefore the answer is $Rs.35$.

Note: In the question initially used the order bucket before the mug. But in the last it is said that $2$ mugs and $3$ buckets. So we can possibly make a mistake by calculating $2x + 3y$ instead of $2y + 3x$ which will lead to a wrong answer.