In a game Rajesh lost 1/3 of his money in the first round of the game, in the second round he losses 3/5 of his remaining money and in the third round he lost 4/7 of the rest. He is left with what part of the original sum of money?

Correct option is B

Given:
Lost of money in the round 1 = 1/3
Lost of money in the round 2 = 3/5 of remaining money
Lost of money in the round 3 = 4/7 of the rest money
Solution:
total money Rajesh has, be the LCM of 3, 5 and 7 just for the convenience of the calculation.
LCM (3, 5, 7) = 105
Hence, let the total money Rajesh has = 105
Money he lost in round 1 = 105 × 1/3 = 35
=> Remaining money after round 1 = 105 - 35 = 70
Money he lost in round 2 = 70 × 3/5 = 42
=> Remaining money after round 2 = 70 - 42 = 28
Money he lost in round 3 = 28 × 4/7 = 16
Now, rest of the money Rajesh has = 28 - 16 = 12
The fraction of money he is left with to the original money = 12/105
= 4/35
Alternate Solution:
original amount of money Rajesh has be x
After the First Round
Rajesh lost ⅓ ​ of his money.
Remaining money after the first round
x- ⅓ ​x = 2/3​ x
After the Second Round
He lost 3/5​ of his remaining money ⅔ x
Amount lost in the second round
⅗ ​× ⅔ x=⅖ ​ x
Remaining money after the second round
⅔ x- ⅖ x
subtract these fractions, we need a common denominator is 15:
⅔ x= 10/15 x And ⅖ x= 6/15 x
Remaining after second round=10/15x-6/15​x=4​/15x
After the Third Round:
He lost 4/7​ of his remaining money (4/15x).
Amount lost in the third round:
4/7×4/15x=16/105x
subtract these fractions, we need a common denominator is 105
4/15 x= 28 / 105 x
Remaining after third round
28/105 x -16/105 x =12/105 x
12/105 x
4/35 x
Fraction of original amount left= 4/35 x /x
= 4/35