Question

A man had a bag of sweets he gave one to his son and 1/7 of the remaining and what he was left he gave to his daughter two sweet and 1/7 of the remaining sweets .The two children found that they have same number of sweets. How many sweets are there in original bag?
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Answer 1

$\mathfrak{Answer:}$

= 36.

$\mathfrak{Step-by-Step\;Explanation:}$

Let the total sweets in the bag be x.

• The son will get sweets :

$\tt{=1+\dfrac{x-1}{7}}\\\\\\\tt{=\dfrac{7+x-1}{7}}\\\\\\\tt{=\dfrac{6+x}{7}.}$

Remaining sweets :

$\tt{=x-\left(\dfrac{6+x}{7}\right)}\\\\\\\tt{=\dfrac{7x-6-x}{7}}\\\\\\\tt{=\dfrac{6x-6}{7}.}$

• The daughter will get sweets :

$\tt{=2+\left(\dfrac{6x-6}{7}-2\right)\times\dfrac{1}{7}}\\\\\\\tt{=2+\left(\dfrac{6x-6-14}{7\times7}\right)}\\\\\\\tt{=\dfrac{98+6x-20}{49}}\\\\\\\tt{=\dfrac{78+6x}{49}.}$

$\mathfrak{According\;to\;Question:}\\\\\\\implies\tt{\dfrac{x+6}{7}=\dfrac{78+6x}{49}}\\\\\\\implies\tt{(x+6)7=78+6x}\\\\\\\implies\tt{7x+42=78+6x}\\\\\\\implies\tt{7x-6x=78-42}\\\\\\\implies\tt{x=36.}\\\\\\\boxed{\boxed{\bold{Total\;no.\;of\;sweets=36.}}}$

Answer 2

Let the original number of sweets in the bag be x .

The man gave "one" sweet to his son and "1/7 th of the remaining".

Since there was x sweet in the beginning , now remaining becomes x - 1 .

So the sweets given away = 1/7 th of x - 1 + 1

⇒ ( x - 1 )/7 + 1

⇒ ( x - 1 + 7 )/7

⇒ ( x + 6 )/7

The son has ( x + 6 )/7 sweet with him .

The daughter was given " two sweets and 1/7 th of the remaining ".

The son has ( x + 6 )/7 sweets .

Remaining sweets = x - ( x + 6 )/7

⇒ ( 7 x - x - 6 )/7

⇒ ( 6 x - 6 ) / 7

Two sweets were given from this .

So now remaining sweets becomes :-

⇒ ( 6 x - 6 )/7 - 2

⇒ ( 6 x - 6 - 14 )/7

⇒ ( 6 x - 20 )/7

1/7 th of the remaining was also given :

⇒ 1/7 × ( 6 x - 20 )/7

⇒ ( 6 x - 20 )/49

The daughter gets ( 6 x - 20 )/49 + 2 sweets .

⇒ ( 6 x - 20 + 98 )/49

⇒ ( 6 x + 78 ) / 49

Given that they have the same number of sweets :-

⇒ ( 6 x + 78 ) / 49 = ( x + 6 ) / 7

⇒ ( 6 x + 78 ) / 7 = x + 6

⇒ 6 x + 78 = 7 x + 42

⇒ 6 x - 7 x = 42 - 78

⇒ - x = - 36

⇒ x = 36

∴ The number of sweets was 36 .