1. **Problem Statement:** Given the total cost of 3 mangoes and 4 apples is 160, and after increasing the cost of a mango by 20% and decreasing the cost of an apple by 20%, the total cost of 5 mangoes and 7 apples is 260. We need to find the original total cost of 1 mango and 2 apples. 2. **Define variables:** Let the original cost of one mango be $x$ and one apple be $y$. 3. **Form equations from given data:** - Total cost of 3 mangoes and 4 apples: $$3x + 4y = 160$$ - After price changes, cost of one mango becomes $1.2x$ and one apple becomes $0.8y$. - Total cost of 5 mangoes and 7 apples after changes: $$5(1.2x) + 7(0.8y) = 260$$ Simplify: $$6x + 5.6y = 260$$ 4. **Solve the system of equations:** From equation 1: $$3x + 4y = 160$$ Multiply by 1.4 to align with second equation coefficients: $$4.2x + 5.6y = 224$$ Subtract this from equation 2: $$6x + 5.6y = 260$$ $$-(4.2x + 5.6y = 224)$$ ------------------------- $$1.8x = 36$$ $$x = \frac{36}{1.8} = 20$$ 5. **Find $y$:** Substitute $x=20$ into equation 1: $$3(20) + 4y = 160$$ $$60 + 4y = 160$$ $$4y = 100$$ $$y = 25$$ 6. **Find the original total cost of 1 mango and 2 apples:** $$x + 2y = 20 + 2(25) = 20 + 50 = 70$$ **Final answer:** The original total cost of 1 mango and 2 apples is **70**. This corresponds to option (a).