# Elements of weighted average

As we can see from the above derivation there are five quantities

- Number of members in 1st group (n
_{1}) - Number of members in 2nd group (n
_{1}) - Average of 1st group (A
_{1}) - Average of 2nd group (A
_{2}) - Weighted average (A
_{w})

Normally, in the case of weighted average, we get questions in which one of these five elements is missing, and with the help of the remaining four quantities, the value of that missing quantity is found. Different possibility (situations) are given below (Y represents âˆ’ data given, N represents âˆ’ data not given):

# First Situation

Example

10 kg of rice priced at Rs 12 per kg is mixed with 6 kg of rice priced at Rs 16 per kg. What is the average price of the whole mixture?

Solution

Lower priced value = Rs 12 per kg and its quantity = 10 kg
Higher priced value = Rs 16 per kg and its quantity = 6 kg
Using Alligation,

, or, A
However, in my opinion, in this situation it is better to use the normal method rather than using the weighted average method of finding A
Normal method âˆ’ Total value = 12 Ã— 10 + 16 Ã— 6 = 216
So, average price = = Rs 13.5/kg

, or, A

_{w}= Rs 13.5/kg_{w.}# Second/Third Situation

Example

Two varieties of rice are mixed in the ratio 2:3. The price of the mixture is Rs 12 per kg and the price of the variety having lower weight is Rs 10 per kg. Find the price of the other variety.

Solution

Now,
So, N = Rs 13.33 per kg

# Fourth/Fifth Situation

Example

Some articles are purchased for Rs 450. 1/3rd of the articles are sold at a loss of 10%. At what percentage profit should the remaining articles be sold to obtain a net profit of 20% on the whole transaction?

Solution

Now, = [20 âˆ’ (âˆ’10)]/[
So,
It is seen that the quantities are in the ratio of 1:2, so the deviation from mean percentage profit in the loss percentage and profit percentage will also be same.
2 corresponds to 30%, so 1 will correspond to 15%. So,

*x*âˆ’ 20]*x*= 35%*x*= 35%# Sixth Situation

Example

Two different qualities of sugar are mixed in some ratio. The price of one quality of sugar is Rs 16/kg and that of another quality is Rs 21/kg. In what ratio have the sugar of two qualities been mixed if the price of the mixture is Rs 19/kg?

Solution

So, the ratio of quantity of sugar of different qualities = 2:3