Multiple choice

Directions: Answer the questions on the basis of the information given below. Emmu, a shopkeeper, has seven items – P, Q, R, S, T, U and V – in his shops. The cost prices of items are Rs. 80, Rs. 90, Rs. 120, Rs. 100, Rs. 75, Rs. 60 and R 125, not necessarily in the same order. The selling prices (in binary system) of the given items are Rs. 111100, Rs. 10010110, Rs. 1001011, Rs. 1111101, Rs 10101111, Rs. 1100100 and Rs. 110000, not necessarily in the same order. It is also known that: (i) The cost price of T, which is sold at a profit less than 30%, is equal to the average of the cost price of Q and that of V. (ii) The profit made on one of the items is twice the amount of profit made on exactly two other items. (iii) The selling price of the item on which the shopkeeper incurs a loss of 16.67% is 40% less than the cost price of P. (iv) The profit made on the item that is sold at Rs. 150 is 25%. (v) The profit (in base 8) on the item that is sold at Rs.175 is Rs. 62. (vi) The cost price of item R is 50% more than the cost price of U. (vii) All the given numbers are in decimal system unless otherwise is mentioned. What is the cost price of S?

  1. Rs. 75

  2. Rs. 125

  3. Rs. 100

  4. Cannot be determined
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AI explanation

Convert the given binary selling prices to decimal to get the set of values 60, 150, 75, 125, 175, 100, and 48. Using condition 4, the item with a cost price of 120 has a selling price of 150. Using condition 5, the item with a selling price of 175 has a cost price of 125 because its octal profit of 62 converts to a decimal profit of 50. Condition 3 indicates an item with a loss of 16.67 percent has a selling price of 48, which equals 0.8333 times its cost price, making its cost price 60, and this 48 is 40 percent less than the cost price of P, making the cost price of P equal to 80. Condition 6 states the cost price of R is 1.5 times the cost price of U, matching the remaining pair of 90 and 60, so R is 90 and U is 60. By condition 1, the cost price of T equals the average of Q and V, utilizing the remaining cost prices 100, 75, and 125, which means T is 100, Q is 75, and V is 125. Having assigned the cost prices for all other items, the cost price of S is 75.

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