Question

Suppose 2 kg of sugar contains $9 \times {10^6}$ crystals.
How many sugar crystals are there in 5 kg of sugar?
(A) 22500000
(B) 27600000
(C) 21850000
(D) 24500000

Answer 1

Hint: We can solve this question by applying the Unitary method of solving. In this method, we first determine the number of sugar crystals in 1 kg of sugar and then multiply the answer by the required number of kg of sugar; in this case, that number is 5.

Complete step-by-step answer:
The number of crystals in 2 kg of sugar are $9 \times {10^6}$ crystals and we have to find the number of sugar crystals in 5 kg of sugar. . Now using the Unitary method of solution and solving step by step, we have-
Then, the number of crystals in 2 kg of sugar
 $ = 9 \times {10^6}$
The number of crystals in 1 kg of sugar
 \[\begin{array}{c}
 = \dfrac{{9 \times {{10}^6}}}{2}\\
 = 4.5 \times {10^6}
\end{array}\]
Now, the number of crystals in 5 kg of sugar is the product of the number of crystals in 1 kg of sugar and 5
So, we get, the number of crystals in 5 kg of sugar
 \[\begin{array}{c}
 = 4.5 \times {10^6} \times 5\\
 = 22.5 \times {10^6}\\
 = 22500000
\end{array}\]
Therefore, there are 22500000 sugar crystals in 5 kg of sugar and the correct option is-
(A) 22500000
So, the correct answer is “Option a”.

Note: An alternative method of solving this question is to use the Proportions method by assuming the number of sugar crystals to be \[x\] and then using the direct proportion given as-
\[\dfrac{2}{{9 \times {{10}^6}}} = \dfrac{5}{x}\]
Now solving this we get,
\[x = 22500000\]
So, the number of sugar crystals in 5 kg of sugar by solving this method we get is 22500000 crystals.