In a shop, five articles — P, Q, R, S and T — are to be sold. The cost price and the selling price of each of the five articles are among Rs.650, Rs.700, Rs.750, Rs.850 and Rs.900. The cost price of each of the articles is different and also the selling price of each of the articles is different. For any article, the selling price is not equal to its cost price.
(1) The cost price of article R is equal to the selling price of article T. While selling R as well as T the shopkeeper incurred a loss.
(2) The cost price of Q is more than that of S and the shopkeeper obtained a profit by selling Q.
(3) The profit made by selling any article is more than R350. The profit made on any two articles is not the same. The loss incurred on any two articles is not the same.
(4) On only two articles, the shopkeeper made a profit. The profit/loss made on any article is not Rs.150.
Let us represent the given information as follows:
| P | Q | R | S | T |
Profit/loss | | profit | loss | | loss |
Cost price (in Rs.) | | b | a | b- | a+ |
Selling price (in Rs.) | | b+ | a- | | a |
Difference | | | | | |
Given profit > 50 and profit at 150.
Therefore, the profits can be any two among 100, 200 and 250.If one of the profits is 250, then the other profit cannot be 200.
Since 250 = 900 — 650 and 200 = 850 — 650 or 900 - 700, which is not possible.
One profit is 100 and the other is 200/250. Also 100 = 750 — 650 or 850 — 750
As neither R nor T made a profit and either the selling price or the cost price of the article, on which the profit made is Rs.100, is Rs. $750 , a \neq 750 .$
As $a + > a > a - , a \neq 650,900$
Therefore, a = 700 or 850
As $b + > b > b - , b \neq 650,900$
If b = 850, then b + must be equal to 900, in which case, the profit is Rs.50, which violates the condition ( 3 ) . Therefore, b = 700 or 750
As profit is greater than R350 and not equal to R3150, the only possibilities for (b, b+) are (700, 900) and (750, 850).
If a = 850, then a+ must be equal to 900. Also. (b, b+)= (700, 900) 2 Profit on selling Q is 200.
$\Rightarrow$ b- must be equal to 650 $\Rightarrow$ On selling a profit is made, that must be equal to 100 .
$\Rightarrow$ The selling price of S is 750.
As the cost price of R is 850, its selling price cannot be 700.
$\Rightarrow$ The selling price of P must be 700, in which case on selling P as well as T the shopkeeper incurred a loss of R350, which violates condition (3).
Hence a=700.
$\Rightarrow a -$ must be equal to 650
$( b , b + ) = ( 750,850 ) \Rightarrow$ on selling Q a profit Rs .100 is made.
$\Rightarrow b -$ must be equal to 650
Therefore, on selling S, a profit is made.
$\Rightarrow$The selling price of S must be $900 ,$ since the profit made on no two articles is the same.
$\Rightarrow$ The selling price of P is Rs.750.
From condition (4) the cost price of P cannot be R3900
Thus, the cost price of P is R3850 and that of T is Rs.900.
Therefore, the final distribution is as follows:
| P | Q | R | S | T |
Cost price (in Rs.) | 850 | 750 | 700 | 650 | 900 |
Selling price (in Rs.) | 750 | 850 | 650 | 900 | 700 |
Q1. The selling price of P is R3750. Choice (2)
Q2. The required difference = 900 - 650 = 250. Choice (2)
Q3. The selling price of T is R3700. Choice (4)
Q4. Only choice (3) is true. Choice (3)
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