Question

State True or False.

If the total cost of $2$ apples and $3$ mangoes is Rs. $22$, then the cost of each apple and each mango must be Rs. $5$ and Rs. $4,$ respectively, (where the cost of each apple and mango is an integer).

• A. True
• B. False

Answer 1

The correct option is B False

Let $x$ represent the cost of each apple and $y$ represent the cost of each mango.
$2x+3y=22......\left(1\right)$
Given that the cost of each apple and each mango must be Rs.5 and Rs.4.
$\therefore 2\left(5\right)+3\left(4\right)\Rightarrow 10+12\Rightarrow 22$
which is equal to LHS of $\left(1\right)$
Also, by substituting the value of $x$ as 2 and $y$ as 6.
$\Rightarrow 2\left(2\right)+3\left(6\right)\Rightarrow 4+18\Rightarrow 22$
which is equal to LHS of $\left(1\right)$
And also by substituting the value of $x$ as 8 and $y$ as 2.
$\Rightarrow 2\left(8\right)+3\left(2\right)\Rightarrow 16+6\Rightarrow 22$
which is equal to LHS of $\left(1\right)$
$\therefore$ the cost of each apple and each mango must not be Rs.5 and Rs.4 since there are many values which satisfy the given equation.
The correct answer is B.