Easy does it! The Smart Scholar Method:

Let the price of an apple, a pear and a mango in Rupees be a, p and m respectively. 5a + 3p = 19, 3a + 4m = 10 and 2p + 3m = 9. Look at the equations a little closer:

5a      +        3p                                              = 19
3a                                    +        4m               = 10

________ 2p                +        3m               =   9

Adding:
8a      +        5p                +        7m               = 38

There you are!

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