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
Correct Answer: 66
Solution and Explanation
Let the number of apples be $5x$, mangoes be $2x$, and the number of oranges be $y$. So, the total number of fruits is:
$5x + 2x + y = 187$ or $7x + y = 187$ (Equation 1).
After selling, the unsold apples are $5x - 75$, mangoes $2x - 26$, and oranges $\frac{y}{2}$. The ratio of unsold apples to unsold oranges is given as 3 : 2:
$\frac{5x - 75}{\frac{y}{2}} = \frac{3}{2}$
Simplifying, we get:
$2(5x - 75) = 3y$ or $10x - 150 = 3y$ (Equation 2).
Now solve the system of two equations: 1. $7x + y = 187$ 2. $10x - 150 = 3y$
From Equation 1, solve for $y$:
$y = 187 - 7x$.
Substitute this into Equation 2:
$10x - 150 = 3(187 - 7x)$,
$10x - 150 = 561 - 21x$,
$31x = 711$,
$x = 23$.
Now, substitute $x = 23$ into Equation 1 to find $y$:
$7(23) + y = 187$,
$161 + y = 187$,
$y = 26$.
Now, the unsold fruits are: Apples: $5(23) - 75 = 115 - 75 = 40$.
Mangoes: $2(23) - 26 = 46 - 26 = 20$.
Oranges: $\frac{26}{2} = 13$.
The total number of unsold fruits are:
$40 + 20 + 13 = 66$.
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