Question

Find the greatest weight which can be contained exactly in 3kg 7hg 8dag 1g and 9kg 1hg 5dag 4g.
A. 1hg 9dag 9g
B. 1hg 8dag 9g
C. 2hg 8dag 8g
D. 2hg 9dag 9g

Answer 1

Hint:- We can change the given weights in a single unit and then find the HCF of them by splitting each weight into prime factors. And products of common prime factors will be HCF of the weights.
As we know that,
1 kg = 1000 g
1 hg = 100 g
1 dag = 10 g

Complete step-by-step answer:
So, now let us change the given weights in grams (g).
So, 3kg 7hg 8dag 1g will be = \[\left( {3 \times 1000} \right) + \left( {7 \times 100} \right) + \left( {8 \times 10} \right) + 1 = 3000 + 700 + 80 + 1 = 3781\] g.
And, 9kg 1hg 5dag 4g will be =\[\left( {9 \times 1000} \right) + \left( {1 \times 100} \right) + \left( {5 \times 10} \right) + 4 = 9000 + 100 + 50 + 4 = 9154\] g.
So, we had to find the greatest weight which can be contained exactly in 3781 g and 9154 g.
And the greatest weight which can be contained will be the HCF of 3781 and 9154.
Now to find the HCF of two numbers we had to split them into the product of prime factors and the HCF will be the product of those factors which are common to both numbers.
So, splitting both numbers as the product of prime factors.
\[3781 = 19 \times 199\]
\[9154 = 2 \times 23 \times 199\]
So, the common factors of 3781 and 9154 will be 199 i.e. the HCF of 3781 and 9154 will be 199.
 So, 199g will be the greatest weight which can be contained exactly in 3kg 7hg 8dag 1g and 9kg 1hg 5dag 4g.
Now we had to change 199 grams into hg, deg because the options are given in hg, deg, and g.
So, 100 grams = 1hg
10 grams = 1deg
So, \[199 = \left( {1 \times 100} \right) + \left( {9 \times 10} \right) + \left( {9 \times 1} \right)\] = 1hg 9deg 9g
Hence, the correct option will be A.

Note:- Whenever we come up with this type of problem then first, we have to change the given weights into the smallest possible unit in the weights (here grams). And after that to find the greatest weight that can be obtained, we had to find the HCF of both the numbers. Now to find the HCF of two numbers there is also an alternate method known as the Euclid algorithm to find the greatest common divisor. Now we had to again change the unit of HCF from grams to hg, deg and g to get the required answer.