Sujatha buys 8 apples and 5 mangoes for ₹ 208. When the cost of an apple is increased by 20% and mango is decreased by 10%, then she can buy 5 apples and 10 mangoes for ₹ 219. What is the cost of 4 apples and 7 mangoes?
Question
Sujatha buys 8 apples and 5 mangoes for ₹ 208. When the cost of an apple is increased by 20% and mango is decreased by 10%, then she can buy 5 apples and 10 mangoes for ₹ 219. What is the cost of 4 apples and 7 mangoes?
Solution
Let's denote the cost of an apple as 'a' and the cost of a mango as 'm'.
From the first sentence, we can form the equation: 8a + 5m = 208.
From the second sentence, we know that the cost of an apple increased by 20% and the cost of a mango decreased by 10%. So, we can form the equation: 5(a + 0.2a) + 10(m - 0.1m) = 219.
Solving these two equations will give us the values of 'a' and 'm'.
Once we have the values of 'a' and 'm', we can find the cost of 4 apples and 7 mangoes by substituting 'a' and 'm' into the equation: 4a + 7m.
Let's solve the equations:
- 8a + 5m = 208
- 5(1.2a) + 10(0.9m) = 219
Solving these equations, we get: a = ₹16 and m = ₹24
Substituting these values into the equation 4a + 7m, we get: 4(16) + 7(24) = ₹64 + ₹168 = ₹232
So, the cost of 4 apples and 7 mangoes is ₹232.
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