Question

40 bags of cotton cost ₹2200, but by exchanging 25 bags with the shopkeeper we get 30 grams of silver. Find the price of 150g of silver by exchanging relevant number of cotton bags.

• A. ₹6875
• B. ₹6675
• C. ₹6575
• D. ₹6975

Answer 1

The correct option is A ₹6875

Number of cotton bags and their price vary directly and so do the amount of silver and its price.
In this problem, we need to use the concept of direct variation twice.
First, we need to find the price of 25 bags of cotton for exchanging silver. Let that price be x (in ₹).
40 bags of cotton cost ₹2200.

Number of cotton bags	Price (in ₹)
40	2200
25	x

Using the arrow method, we get
$\frac{25}{40}=\frac{x}{2200}$

This gives x = $\frac{25}{40}\times 2200$
= ₹1375, which is the price of 30 grams of silver.

Let the price of 150 grams of silver be ₹y. We will again apply direct variation.

Quantity of silver (in grams)	Price (in ₹)
30	1375
150	y

Using the arrow method, we get
$\frac{150}{30}=\frac{y}{1375}$

This gives y = $\frac{150}{30}\times 1375$
= ₹6875, which is the price of 150 grams of silver.