a merchant instructs his agent to buy 1000 pens and sell them at 15% above the purchase price. The agent charges 1% commission on purchase and 3% commission on sales and earns 534 as commission. Find the price at which agent buys pen.
Answers
Answer:
No. of Pens= x
CP of 1000 Pens=1000 x
Sp. Pens=1000x115/100
= 1150x
Com.on Purchase = 1000Xxl/100
= 10x
com.on sales = 1150x3/100
=34.5x
Total com.=1 0x+34.5x=44.5x=534
44.5x=534
x = 534 / 44.5=12
Agent buys pen@ Rs 12. Ans
cost. Price of 1,000 pens=,1000x12
= Rs 12000
Given,
Number of pens purchased by a merchant through his agent = 1000
He sells them at 15% above the purchase price.
Agent's commission on purchase = 1%
Agent's commission on sales = 3%
Total amount earned by the agent as the commission = Rs. 534
To find,
The price at which the agent buys the pen.
Solution,
We can simply solve this mathematical problem using the following process:
Let us assume that the cost price of each one is Rs. x.
Now, according to the question;
The total cost price of all the pens purchased = Rs. 1000x
And, the total selling price of all the pen
= 15% above the purchase price
= Rs. {1000x + (15/100×1000x)}
= Rs. 1150x
Now, according to the question;
The total commission charged by the agent on the purchase
= 1% of the cost price of all the pens purchased
= Rs. (1/100×1000x)
= Rs. 10x
The total commission charged by the agent on the sales
= 3% of the selling price of all the pens purchased
= Rs. (3/100×1150x)
= Rs. 34.5x
Now, according to the question;
(Total commission charged by the agent on the purchase) + (Total commission charged by the agent on the sales) = Rs 534
=> Rs. 10x + Rs. 34.5x = Rs 534
=> 44.5x = 534
=> x = 534/44.5 = 12
=> The cost price of each pen = Rs. 12
Hence, the agent buys the pen at Rs. 12 per each.