Thank you so much,
what if the numbers could not be simplified? is there a simple way to do it to get a rough figure without too much computations?

amyhussein wrote:hello
how to solve the following question in a shorter simpler way

there is a total of 48 items with average cost of 51. The average cost of 32 items is 39 usd, what is the average cost of the remaining 16 items?

Approach 1: Plug in small values that satisfy the given ratio
32 items cost an average of $39, while the remaining 16 items cost an average of x dollars.
Since 32:16 = 2:1, for every 2 items that cost $39, 1 item costs x dollars.
Total cost of 3 items at an average cost of $51 per item = 3*51 = 153.
Total cost of 2 items at an average cost of $39 per item = 2*39 = 78.
Cost of the 1 remaining item = 153-78 = 75.

Approach 2: alligation
Let A = the $39 items and B = the items with an unknown average cost.

Step 1: Plot the costs on a number line, with the two ingredients on the ends and the average cost of the mixture in the middle.
A 39----------51---------B

Step 2: Plot the distances between the costs.
(distance between A and 51) : (distance between 51 and B) is equal to the RECIPROCAL of the ratio of A to B in the mixture.
Since A = 32 items and B = 16 items, A:B = 32:16 = 2:1.
Plotting the reciprocal of this ratio on the number line, we get:
A 39----x-----51----2x----B

Since x is the distance between A and 51:
x = 51-39 = 12.
Since 2x is the distance between 51 and B:
B = 51 + 2x = 51 + 2*12 = 75.

Other mixture problems:

https://www.beatthegmat.com/a-charitable ... 88187.html
https://www.beatthegmat.com/mixture-prob ... tml#604126
https://www.beatthegmat.com/mixture-prob ... 90121.html
https://www.beatthegmat.com/algebra-t195034.html

amyhussein wrote:hello
how to solve the following question in a shorter simpler way

there is a total of 48 items with average cost of 51. The average cost of 32 items is 39 usd, what is the average cost of the remaining 16 items?

Here's a quick way in my opinion -

Given that average cost of 48 items is 51$.

Now , The average cost of 32 items is 39$ & average cost of the remaining 16 items will definitely be greater than 51$. Because -"The loss incurred because of the first group must be compensated by the second group." Make sense?


We want to have an average of51$ , but first group managed only 39$ . So we lost an average of 12 upon 32 Items . hence, the loss in the sum = 32*12 =384$

Now this loss of 384$ must be compensated by our second group i.e.16 Items.

So their average must be not only the initial 51$, but also the average meant to compensate the loss incurred because of the first group.

Hence the average of the remaining 16 Items = 51 + 384 / 16 = 75 .

OA - 75

Hope it make sense ?