Question

Three small water bottles and five large water bottles can hold \[17\] litres of water. Two large water bottles minus one small water bottle constitute $9$ litres of water. How many litres of water can one large water bottle hold?
A) $4$
B) $3$
C) $2$
D) $1$

Answer 1

Hint: Capacities of a set of water bottles can be obtained by adding individual capacities. By expressing the given data in mathematical equations and solving it we can find the capacity of larger and smaller water bottles.

Formula used: If the capacities of some containers are ${x_1},{x_2},...,{x_n}$ , then the total capacity is ${x_1} + {x_2} + ... + {x_n}$ units. Also, if the capacity of a container is $x$ units, then the total capacity of $k$ identical containers is $kx$ units.

Complete step-by-step answer:
Given that three small water bottles and five larger water bottles can hold $17$ litres of water and two large water bottles minus one small water bottle can hold $9$ litres of water.

Let the capacity of a small water bottle be $x$ litres and the capacity of a large water bottle be $y$ litres.
Then the capacity of $3$ small bottles and $5$ large bottles is $3x + 5y$
Also, the capacity of $2$ large bottles minus $1$ small bottle is $2y - x$
Substituting these in the given information we have,
$3x + 5y = 17 - - - (i)$
$2y - x = 9 - - - - (ii)$
Rearranging the $(ii)$ equation,
$3x + 5y = 17 - - - (i)$
$ - x + 2y = 9 - - - (ii)$
Now we have $2$ equations in $2$ variables.

By multiplying the second equation by $3$ and adding the $2$ equations we can eliminate the variable $x$ .
Multiplying equation $(ii)$ by $3$ we have,
$3x + 5y = 17 - - - (i)$
$ - 3x + 6y = 27 - - (ii)$
Adding $(i)$ and $(ii)$ we get,
$3x - 3x + 5y + 6y = 17 + 27$
$ \Rightarrow 0x + 11y = 44$
$ \Rightarrow 11y = 44$
Dividing both sides of the above equation by $11$ we get,
$\dfrac{{11y}}{{11}} = \dfrac{{44}}{{11}}$
$ \Rightarrow y = 4$
‘$y$’ indicates the capacity of a large bottle.
$\therefore $ The capacity of a large bottle is $4$ litres.

So, the correct answer is “Option A”.

Note: The set of equations in two variables can also be solved by expressing one variable in terms of the other using one equation and substituting in the next. The point should be noted is that the given quantities are in the same unit or not. Here the capacity of both bottles is expressed in litres.