Question

A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes and half of the oranges, the ratio of number of unsold apples to number of unsold oranges becomes 3 : 2. The total number of unsold fruits is

Answer 1

Correct Answer: 66

Let $5x$ be the number of apples, $2x$ be the number of mangoes, and $y$ be the number of oranges. The total number of fruits is:

$5x + 2x + y = 187$, which simplifies to $7x + y = 187$ (Equation 1).

After selling, the remaining fruits are: apples ($5x - 75$), mangoes ($2x - 26$), and oranges ($\frac{y}{2}$). The ratio of unsold apples to unsold oranges is 3:2:

$\frac{5x - 75}{\frac{y}{2}} = \frac{3}{2}$

This simplifies to:

$2(5x - 75) = 3y$, or $10x - 150 = 3y$ (Equation 2).

We now solve the system of two equations: 1. $7x + y = 187$ and 2. $10x - 150 = 3y$.
From Equation 1, we can express $y$ as:

$y = 187 - 7x$.

Substitute this expression for $y$ into Equation 2:

$10x - 150 = 3(187 - 7x)$,
$10x - 150 = 561 - 21x$,
$31x = 711$,
$x = 23$.

Now, substitute $x = 23$ back into Equation 1 to find $y$:

$7(23) + y = 187$,
$161 + y = 187$,
$y = 26$.

The number of unsold fruits are: Apples: $5(23) - 75 = 115 - 75 = 40$.Nbsp;
Mangoes: $2(23) - 26 = 46 - 26 = 20$.Nbsp;
Oranges: $\frac{26}{2} = 13$.
The total number of unsold fruits is:

$40 + 20 + 13 = 66$.