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.

If Roopa leaves home with 30 flowers, the number of flowers she offers to each deity is:

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Solution

The correct option is C 32
Let Roopa have x flowers with her; then

$\begin{matrix} B a l a n c e b e f o r e o f f e r i n g & F l o w e r s o f f e r e d & B a l a n c e a f t e r o f f e r i n g I^{s t} P l a c e & 2 x & y & 2 x - y I I^{n d} P l a c e & 4 x - 2 y & y & 4 x - 3 y I I I^{r d} P l a c e & 8 x - 6 y & y & 8 x - 7 y I V^{t h} P l a c e & 16 x - 14 y & y & 16 x - 15 y \end{matrix}$

$16 x - 15 y = 0 \Rightarrow 16 x = 15 y \Rightarrow y = \frac{16 x}{15}$

If $x = 30, t h e n y = 16 \times 2 = 32$ .

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Similar questions

Q. 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:

Q. If Roopa leaves home with 30 flowers, the number of flowers she offers to each deity is : (CAT 1999)

Q. Radha takes some flowers in a basket and visit three temples one by one. At each temple, she offers one half of the flowers from the basket. If she is left with

3

flowers at the end, find the number of flowers she had in the beginning.

Solve the following:
Radha takes some flowers in a basket and visits three temples one-by-one. At each temple, she offers one half of the flowers from the basket. If she is left with $3$ flowers at the end, then find the number of flowers she had in the beginning.

Q. The minimum number of flowers that could be offered to each deity is : (CAT 1999)

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The correct option is C 32Let 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⇒y=16x15 If x=30, then y=16×2=32.