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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 _________.
Correct Answer: 50
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
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