Question

Arpit has some marbles in his bag. He puts half of the
marbles 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

$\huge{\bold{\underline{\underline {\mathfrak{Answer:}}}}}$

Number of marbles in the jar = 30

$\underline {\underline{\bold {\mathfrak{Step-by-step\:explanation:}}}}$

Given:-

• Arpit has some marbles in his bag.
• He put half of the marbles in a jar and one-sixth in his pocket.
• Total number of marbles are 10 more than twice of the remaining marbles in the bag.

Find:-

• Number of marbles in the jar.

Solution:-

Let the -

• total number of marbles be "M"

Arpit put half of the matbles in the jar.

So, number of marbles in the jar = $\sf{\frac{M}{2}}$

Also, he put one-sixth of the marbles in his pocket.

So, number of marbles in his pocket = $\sf{\frac{M}{6}}$

$\therefore$ Remaining marbles = Total number of marbles - (Marbles in the jar + marbles in his pocket)

=> $\sf{M\:-\:(\frac{M}{2}\:+\:\frac{M}{6}})$

=> $\sf{M\:-\:(\frac{3M\:+\:M}{6})}$

=> $\sf{M\:-\:\frac{4M}{6}}$

=> $\sf{\frac{6M\:-\:4M}{6}}$

=> $\sf{\frac{2M}{6}}$

=> $\sf{\frac{M}{3}}$

Total marbles are 10 more than twice of the remaining marbles in the bag.

According to question,

=> $\sf{M\:=\:10\:+\:2(\frac{M}{3})}$

=> $\sf{M\:=\:10\:+\:\frac{2M}{3}}$

=> $\sf{M\:-\:\frac{2M}{3}\:=\:10}$

=> $\sf{\frac{3M\:-\:2M}{3}\:=\:10}$

=> $\sf{M\:=\:10(3)}$

=> $\sf{M\:=\:30}$

•°• Total number of marbles in the jar is 30.

Answer 2

Answer:

30

Step-by-step explanation:

let the number of marbles be x

In jar = x/2

In his pocket = x/6

Remaining marbles = x/3

ATQ

x = 10 + 2(x/3)

x = 30