Question

At the Rice Research Centre at Tumsar, there are $2610$ kg of seeds of the basmati variety and $1980$ kg of the Indrayani variety. If the maximum possible weight of seeds has to be filled to make bags of equal weight what should be the weight of each bag ? How many bags of each variety will there be ?

Answer 1

Weight of the seeds of basmati rice $=2610$ kg
Weight of the seeds of Indrayani rice $=1980$ kg
The maximum possible weight of each bag that can be filled with seeds of each variety of rice is the HCF of $2610$ and $1980$ in kilogram.
Factors of $2610:1,2,3,5,6,9,10,15,18,29,30,45,58,87,90,145,174,261,290,435,522,870,1305,2610$
Factors of $1980:1,2,3,4,5,6,9,10,11,12,15,18,20,22,30,33,36,44,45,55,60,66,90,99,110,132,165,180,198,220,330,396,495,660,990,1980$
Common factors of $2610$ and $1980:1,2,3,5,6,9,10,15,18,30,45,90$
HCF of $2610$ and $1980=90$
∴ Maximum possible weight of each bag that can be filled with seeds of each variety of rice $=90$ kg
Thus, the maximum weigth of each bag should be $90$ kg.
Also,
Number of bags filled with the seeds of basmati rice $=\frac{2610}{90}=29$
Number of bags filled with the seeds of Indrayani rice $=\frac{1980}{90}=22$
Thus, the number of bags filled with the seeds of basmati rice and Indrayani rice are $29$ and $22$ respectively.