Shortcut:
If a person sells an item 'A' at a profit of a1% and the other item 'B' at a loss of b1%, but on the whole he gains Rs Z. On the other hand if he sells the item 'A' at a loss of b2% and the item 'B' at a profit of a2%, then he neither gains nor loses, then the
(i) Cost price of A is Rs
Z x a1
/
a1xa2 − b1 x b2
x 100
(ii) The cost price of B is Rs
Z x b1
/
a1xa2 − b1xb2
x 100.
Here, a1 = 12
1
/
2
or
25
/
2
, b1 = 8
1
/
3
or
25
/
3
, a2 = 12
1
/
2
or
25
/
2
, b2 = 8
1
/
3
or
25
/
3
, Z = 25
Using these value in shortcut, we get:
Cost Price of table = Rs
25 x 25/2
/
(25/2 x 25/2) − (25/3 x 25/3)
x 100 = Rs 360
Hence, cost price of the table be Rs 360.
Cost Price of chair = Rs
25 x 25/3
/
(25/2 x 25/2) − (25/3 x 25/3)
x 100 = Rs 240
Hence, cost price of the table be Rs 240.
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