Question

Two tankers contain 240 litres and 180 litres of kerosene oil respectively. Find the maximum capacity of a container which can measure the kerosene oil of both the tankers when used an exact number of times.

Answer 1

Answer:

60 litres

Explanation:

Given :

Two tankers of kerosene are of 240 and 180 litres.

To Find :

Maximum capacity of containers to measure both tankers.

Solution :

Measuring capacity =  HCF of 240 and 180

So,

$\begin{array}{r | l} 2 & 240 \\ \cline{1-2} 2 & 120 \\ \cline{1-2} 2 & 60 \\ \cline{1-2} 2 & 30 \\ \cline{1-2} 3 & 15 \\ \cline{1-2} 5 & 5 \\ \cline{1-2} 1 & 1 \end{array}$

$\begin{array}{r | l} 2 & 180 \\ \cline{1-2} 2 & 90 \\ \cline{1-2} 3 & 45 \\ \cline{1-2} 3 & 15 \\ \cline{1-2} 5 & 5 \\ \cline{1-2} 1 & 1 \end{array}$

240 = 2 × 2 × 2 × 2 × 3 × 5

180 = 5 × 2 × 2 × 3 × 3

HCF of 240 and 180 = 60

Therefore,maximum mesuring capacity = 60 litres

To fill 240 litre, we have to measure 4 times  [60 × 4]

To fill 180 litre, we have to measure times  [60 × 3]

Answer 2

Step-by-step explanation:

Maximum measuring capacity = HCF of 240 and 180

HCF of 240 and 180 :

$\rule{170}1$

$\begin{array}{c|c}\sf2&\sf 240 \\ &\dfrac{\qquad \qquad \qquad \qquad \quad}{} \\\sf2&\sf 120 \\ &\dfrac{\qquad \qquad \qquad \qquad \quad}{} \\\sf2&\sf 60 \\ &\dfrac{\qquad \qquad \qquad \qquad \quad}{} \\\sf2&\sf 30\\&\dfrac{\qquad \qquad \qquad \qquad \quad}{} \\\sf3&\sf 15 \\ &\dfrac{\qquad \qquad \qquad \qquad \quad}{} \\\sf5&\sf 5 \\ &\dfrac{\qquad \qquad \qquad \qquad \quad}{} \\&\sf1 \end{array}$

$\rule{170}1$

$\begin{array}{c|c}\sf2&\sf 180 \\ &\dfrac{\qquad \qquad \qquad \qquad \quad}{} \\\sf2&\sf 90 \\ &\dfrac{\qquad \qquad \qquad \qquad \quad}{} \\\sf3&\sf 45 \\ &\dfrac{\qquad \qquad \qquad \qquad \quad}{} \\\sf3&\sf 15 \\ &\dfrac{\qquad \qquad \qquad \qquad \quad}{} \\\sf5&\sf 5 \\ &\dfrac{\qquad \qquad \qquad \qquad \quad}{} \\&\sf1 \end{array}$

$\rule{170}1$

Hence,

240 = 2 × 2 × 2 × 2 × 3 × 5

180 = 2 × 2 × 3 × 3 × 5

$\therefore\:\underline{\sf{HCF = 2 \times 2 \times 3 \times 5 = \textbf{60}}}.$

$\textsf{So maximum measuring capacity is = \textbf{60 litres}}.$

$\rule{170}2$

$\begin{lgathered}\bullet\:\:\sf{To \:fill\: 240\: litres,\: we\: measure\: 4 \:times\: =\: 60 \times 4 = \textbf{240}}\\\\\bullet\:\:\sf{To\: fill \:180\: litres, \:we\: measure\: 3 \:times = 60 \times 3 = \textbf{180}}\end{lgathered}$