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.

Answer 1

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.