Question

The cost price of item B is Rs. 150/- more than the cost price of item A. Item A
was sold at a profit of 10% and item B was sold at a loss of 20%. If the respective
ratio of selling prices of items A and B is 11 : 12, what is the cost price of item B?
(1) Rs. 450/-
(2) Rs. 420/-
(3) Rs. 400/-
(4) Rs. 350/-
(5) Rs. 480/-

Answer 1

Let the cost price of the Item A be Rs. x.
∴ Cost Price of the Item B = Rs. x + 150

For Item A, 
S.P. = [(100 + P%)/100] C.P.
   = [(100 + 10)/100]x
  = 110x/100 × 
  = Rs. 11x/10


For Item B, 
S.P. = [(100 - L)/100]C.P.
       = [(100 - 20)/100](x + 150)
       = 80/100 × (x + 150)
       = Rs.8(x + 150)/10 


As per as the Question, Ratio of the Selling Price of the Item A and B is 11:12

∴ (11x/10) ÷ 8(x + 150)/10 = 11/12
⇒  11x/(8x + 1200) = 11/12
⇒ 132x = 88x + 13200
⇒ 44x = 13200
∴ x = Rs. 300


Hence, the C.P. of the Item A is Rs. 300. 
∴ C.P. of the Item B is 300 + 150 = Rs. 450 


Hence, Option (1). is correct. 


Hope it helps.

Answer 2

Let C.P of A be x

B= 200+x

Sp of A =(120\100)x

Sp of B = (70/100)* (x+200)

On dividing up of A by B

(6x*10/5)/5(7x+1400)=6/7 (given ratio)

We get, x=200.

Therefore, C.P of B= 200+200

= 400 answer