Fruit Seller Ratios

Let the initial number of apples, mangoes, and oranges be $A, M,$ and $O$ respectively. Given $A : M = 5 : 2$, let $A = 5x$ and $M = 2x$. Total initial fruits: $5x + 2x + O = 187 \implies O = 187 - 7x$.

Unsold fruits:

• Unsold apples = $5x - 75$
• Unsold mangoes = $2x - 26$
• Unsold oranges = $\frac{O}{2} = \frac{187 - 7x}{2}$

Given ratio of unsold apples to unsold oranges is $3 : 2$: $\frac{5x - 75}{\frac{187 - 7x}{2}} = \frac{3}{2}$ $2(5x - 75) = \frac{3}{2}(187 - 7x)$ $4(5x - 75) = 3(187 - 7x)$ $20x - 300 = 561 - 21x$ $41x = 861 \implies x = 21$

Substitute $x = 21$:

• Unsold apples = $5(21) - 75 = 30$
• Unsold mangoes = $2(21) - 26 = 16$
• Unsold oranges = $\frac{187 - 7(21)}{2} = \frac{40}{2} = 20$

Total unsold fruits = $30 + 16 + 20 = 66$.