Question

Divide \[182\] in three parts in the ratio $\dfrac{1}{{10}}:\dfrac{1}{{15}}:\dfrac{1}{{20}}.$

Answer 1

Hint: To solve this question, we will start with converting the ratio by taking LCM. Then we will take the sum of the ratio and further divide \[182\] in three parts.

Complete step by step answer:
 We have been given a number \[182;\] we need to divide the given number in three parts in the ratio $\dfrac{1}{{10}}:\dfrac{1}{{15}}:\dfrac{1}{{20}}.$
We will start with converting the given ratio $\dfrac{1}{{10}}:\dfrac{1}{{15}}:\dfrac{1}{{20}}.$
So, L.C.M. of \[\left( {10,15,20} \right){\text{ }} = {\text{ }}60\]
Then, $\dfrac{1}{{10}} \times 60 = 6$
$\dfrac{1}{{15}} \times 60 = 4$
$\dfrac{1}{{20}} \times 60 = 3$
So, the given ratio is in the form $6:4:3.$
Now, sum of \[6,4\] and \[3{\text{ }} = {\text{ }}13\]
So, we get the first part of \[182\] \[ = \] $\dfrac{6}{{13}} \times 182 = 84$
Second part of \[182\] \[ = \] $\dfrac{4}{{13}} \times 182 = 56$
Third part of \[182\] \[ = \] $\dfrac{3}{{13}} \times 182 = 42$
Thus, three parts of \[182\] when divided in the ratio $\dfrac{1}{{10}}:\dfrac{1}{{15}}:\dfrac{1}{{20}}$ is \[84,{\text{ }}56\] and \[42.\]

Note: We have taken the LCM of \[\left( {10,15,20} \right)\] above in the solution. Now let us see the elaborative way of taking LCM given below.

Thus, L.C.M.\[\left( {10,15,20} \right) = 2 \times 2 \times 3 \times 5 = 60\]