Aruna purchases a certain number of apples for INR 20 each and a certain number of mangoes for INR 25 each. If she sells all the apples at 10% profit and all the mangoes at 20% loss, overall she makes neither profit nor loss. Instead, if she sells all the apples at 20% loss and all the mangoes at 10% profit, overall she makes a loss of INR 150 . Then the number of apples purchased by Aruna is _________.

Let, Aruna buys 'a' number of apples and 'm' number of mangoes

So, total C.P. =$$20a+25m$$

In the first case, when she sells all the apples at 10% profit and all the mangoes at 20% loss, total S.P.= $$20a\times\ 1.1+25m\times\ 0.8$$

In this case, she is neither making profit nor loss.

So, total C.P. = total S.P.

or, $$20a+25m=20a\times\ 1.1+25m\times\ 0.8$$

or, $$20a+25m=22a+20m$$

so, $$2a=5m$$ ---->(1)

In the second case, when she sells all the apples at 20% loss and all the mangoes at 10% profit, total S.P. = $$20a\times\ 0.8+25m\times\ 1.1$$

or, Total S.P. = $$16a+27.5m$$

In this case, she made a loss of INR 150.

So, Total S.P.+150 = Total C.P.

or, $$16a+27.5m+150=20a+25m$$

or, $$2.5m+150=4a$$ ----->(2)

Now, from equation (1),

$$2a=5m$$ or, $$a=2.5m$$

Putting this in equation (2), $$a+150=4a$$

or, $$3a=150$$

or, $$a=\dfrac{150}{3}=50$$

So, number of apples purchased by Aruna is 50