A young girl Roopa leaves home with x flowers goes to the bank of a nearby river. On the bank of the river, there are four places of worship, standing in a row. She dips all the x flowers into the river, the number of flowers doubles. Then she enters the first place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the second place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the third place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the fourth place of worship, offers y flowers to the deity. Now she is left with no flowers in hand.
The minimum number of flowers with which Roopa leaves home is:
A young girl Roopa leaves home with x flowers goes to the bank of a nearby river. On the bank of the river, there are four places of worship, standing in a row. She dips all the x flowers into the river, the number of flowers doubles. Then she enters the first place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the second place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the third place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the fourth place of worship, offers y flowers to the deity. Now she is left with no flowers in hand.
The minimum number of flowers with which Roopa leaves home is:
The correct option is B 15
Let Roopa have x flowers with her; then
Balance before offeringFlowers offeredBalance after offeringIst Place2xy2x−yIInd Place4x−2yy4x−3yIIIrd Place8x−6yy8x−7yIVth Place16x−14yy16x−15y
16x−15y=0⇒16x=15y⇒x=15y16
Minimum value of x is available for y = 16. ∴x=1516×16=15.
Let Roopa have x flowers with her; then
Balance before offeringFlowers offeredBalance after offeringIst Place2xy2x−yIInd Place4x−2yy4x−3yIIIrd Place8x−6yy8x−7yIVth Place16x−14yy16x−15y
16x−15y=0⇒16x=15y⇒x=15y16
Minimum value of x is available for y = 16. ∴x=1516×16=15.
