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 = `2610/90 = 29`

Number of bags filled with the seeds of Indrayani rice = `1980/90 = 22`

Thus, the number of bags filled with the seeds of basmati rice and Indrayani rice are 29 and 22, respectively.