Question

Arpit has some marbles in his bag. He puts half of the marble in a jar and one-sixth in his pocket. If total marbles are 10 more than twice of the remaining marbles in the bag, then find the number of marbles in the jar?

Answer 1

If total marbles are 10 more than twice of the remaining marbles in the bag, then the number of marbles in the jar is 30.

Step-by-step explanation:

Let the total no. of marbles in the bag be “x”.

It is given that,

Arpit puts ½ of total marbles in the jar.

So, no. of marbles left in the bag = $\frac{x}{2}$

And,

He puts 1/6th of the marbles remaining in the bag, in his pocket.

So, No. of marble now left in the bag = $\frac{x}{2} - [\frac{1}{6} * \frac{x}{2}] = \frac{x}{2} - \frac{6x - x}{12} = \frac{5x}{12}$

Now,  

According to the question, we can write the equation as,

x = [2*$\frac{5x}{12}$] + 10

⇒ 12x = 10 x + 120

⇒ 2x = 120

⇒ x = $\frac{120}{2}$

⇒ x = 60

Thus,

The no. of marbles in the jar is,

= $\frac{x}{2}$

= $\frac{60}{2}$

= 30

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Answer 2

The number of marbles in the jar is 15.

Step-by-step explanation:

Let the number of marbles in the bag is x.

Given:

• Arpit puts half of the marble in a jar and one-sixth in his pocket.

$\rightarrow \: marbles \: in \: a \: jar \: = \frac{x}{2} \\ \rightarrow \: marbles \: in \: pocket = \frac{x}{6}$

• If total marbles are 10 more than twice of the remaining marbles in the bag.

$\rightarrow \: remaining \: marbles \: = x - ( \frac{x}{2} + \frac{x}{6} ) \\ \rightarrow \: remaining \: marbles = x - \frac{4x}{6} \\ \rightarrow \: remaining \: marbles = \frac{2x}{6} = \frac{x}{3} \\ \rightarrow \: total \: marbles = x = 10 + 2 \times remaining \: marbles \\ \rightarrow \: x = 10 + \frac{2x}{3} \\ \rightarrow \: x - \frac{2x}{3} = 10 \\ \rightarrow \: \frac{x}{3} = 10\\ \rightarrow \:x = 30 \\ \rightarrow \:marbles \: in \: jar \: = \frac{x}{2} = \frac{30}{2} = 15$

The number of marbles in the jar is 15.