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Question
A shopkeeper sells three mobile phones at Rs. 15000, Rs. 9945 and Rs.5392 respectively. He makes a profit of 25% on the first mobile and `10(1)/(2)`% on the second, but incurs an overall loss `8(1)/(3)`% on the 3 whole transactions. Find the cost price of the third mobile.
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Solution
S.P. of the first mobile = Rs.15000, profit = 25%
∴ Rs.15000 = `(1 + 25/100)` of C.P.
= `(5)/(4)` of C.P.
⇒ C.P. = Rs.`(15000 xx 4/5)`
= Rs.12000
S.P. of the second mobile
= Rs.9945, profit
= `10(1)/(2)`%
= `(21)/(2)`%
Rs.9945 = `(1 + (21/2)/100)` of C.P.
= `(221)/(200)` of C.P.
⇒ C.P. = Rs. `(9945 xx 200/221)`
Rs.9000
Let the C.P. of the third article be Rs. x.
∴ C.P. of all the three articles
= Rs.12000 + Rs.9000 + Rs.x
= Rs.(21000 + x)
∴ S.P. of all the three articles
= Rs.15000 + Rs.9945 + Rs.5392
= Rs.30337
As the loss incurred on the whole transaction
= `8(1)/(3)`%
= `(25)/(3)`%
So, Rs.30337 = `(1 (25/3)/100)` of Rs.(21000 + x)
⇒ 30337 = `(1 - 1/12) xx (21000 + x)`
⇒ 30337 = `(11/22) xx (21000 + x)`
⇒ `(364044)/(11)` = 21000 + x
⇒ x = `(133044)/(11)`
= Rs.12095 approximately.
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