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The cost of 3 mangoes and 4 oranges is Rs. 70. If the price of a mango is increased by 20% and that of an orange is decreased by 12%, then the cost of 5 mangoes and 7 oranges is becomes Rs.124.36. What is the initial (price) of 2 mangoes and 3 oranges? 

The cost of 3 mangoes and 4 oranges is Rs. 70. If the price of a mango is increased by 20% and that of an orange is decreased by 12%, then the cost of 5 mangoes and 7 oranges is becomes Rs.124.36. What is the initial (price) of 2 mangoes and 3 oranges?  Correct Answer <span style="">Rs. 49.50</span>

Given:

The cost of 3 mangoes and 4 oranges is Rs. 70.

After increase and decrease in the price of mango and orange the cost of 5 mangoes and 7 oranges is becomes Rs.124.36

Calculation:

Let price of 1 mango be 100a and 1 orange be 100b

So, 300a + 400b = Rs. 70      ----(i)

After increase and decrease in the price of mango and orange,

Mango = 120a

Orange = 88b

600a + 616b = 124.36      ----(ii)

By multiplying 2 with eq (i) we get

600a + 800b = 140      ----(iii)

By subtracting eq (ii) from eq (iii) we get

184b = 15.64

⇒ b = 15.64/184

⇒ 100b = (15.64/184) × 100 = 8.5

⇒ 400b = 8.5 × 4 = 34

Putting the value of 400b in the eq (I) we get

300a = 70 - 34

⇒ 300a = 36

⇒ 100a = 12

Now,

Price of 2 mangoes and 3 oranges = 2 × 12 + 3 × 8.5

⇒ 24 + 25.5

⇒ 49.5

∴ The initial (price) of 2 mangoes and 3 oranges is 49.5

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