Question

1 kg packen of burfee has 16 pieces. \[1kg\] packet of rasgullas has 12 pieces. If we want to buy an equal number of both, and if we can buy only in full packets, what is the least number of each sweet we would have to buy? How many kg of each do we need to buy?

Answer 1

Hint: We are given the number of pieces of sweets for \[1kg\] of both the sweets and we have to buy an equal number of both in full packets. We will take the equal number of pieces bought for each as \[x\] and the number of each kilogram of both the sweets required be \[a\] and \[b\]. To buy an equal number of sweets, it would be possible by taking the least common multiple of the number pieces present in \[1kg\] of both the sweets.

Complete step by step solution:
According to the given question, we have the quantity of sweet present in \[1kg\] of both the sweets, we have,
\[1kg\] of burfee has 16 pieces and \[1kg\] of rasgullas has 12 pieces.
 Let the number of pieces bought for each of the sweets be \[x\] pieces.
And let the number of kilograms of barfi and rasgulla required so that the number of pieces are the same be \[a\] and \[b\] respectively.
That is,
For burfee, the total number pieces we will buy is:
\[x=16\times a\]-------(1)
For rasogulla, the total number pieces we will buy is:
\[x=12\times b\]-------(2)
In order to find the minimum quantity so that both sweets have equal number of pieces, we will take the least common multiple, that is, LCM of 16 and 12.
\[LCM(16,12)=48\]
That is, the total number of pieces bought for each of the sweets is 48.
To determine the amount of both the sweets required we will put the value of x in the equations (1) and (2), we get,
For burfee, we have,
\[x=16\times a\]
\[\Rightarrow 48=16\times a\]
\[\Rightarrow a=3\]
That is, \[3kg\] of burfee is bought.
For rasgulla, we have,
\[x=12\times b\]
\[\Rightarrow 48=12\times b\]
\[\Rightarrow b=4\]
That is, \[4kg\] of rasgulla is bought.
Therefore, the least number of each sweet we would have to buy is 48 pieces.
\[3kg\] of burfee and \[4kg\] of rasgulla is bought.

Note: The question asked for the least number of both the sweets required, that is why we used LCM in our calculations. If the question had been to find the maximum number of both the sweets required, then we would have used HCF, which is
\[HCF(16,12)=4\]
Also, the calculation for the kilograms required for each of the sweets should be done neatly and should not intermix with each other.