Question

Dhanvin is in the habit of saving one-rupee coins given to him by his mother. One day, he
opened his piggy bank and showed the number of one-rupec coins to his father, Rajeev
Rajeev doubled the number of coins and said that Dhanvin should share them equally with
his three brothers. He gave X number of one-rupee coins to his first brother, Yavin and
showed the remaining to Rajeev. Rajeev doubled them again. Then Dhanvin gave the same
X number of one-rupee coins to his second brother, Charan and showed the remaining to
Rajeev. He doubled them again and Dhanvin gave the same X number of one-rupee coins to
Reyansh, the third brother. When he showed the remaining one-rupee coins to Rajeev, he
doubled them again and then Dhanvin had exactly X number of one-rupee coins for himself.

1. If Dhanvin started with 30 one-rupee coins, how many did he give to Yajvin?
A. 30
C. 32
B. 31
D. 33

2. What is the minimum number of one-rupee coins could Dhanvin have started with?
A 15
C. 18
B.16
D. 10

3. If Dhanvin started with 30 one-rupee coins, what is number of one-rupee coins
created (contributed) by Rajeev to all the four brothers?
A. 30
B. 32
C. 128
D.98

4. What is the maximum possible number contributed by Rajeev, to the X one-rupee
coins received by Yajvin, if Dhanvin started with 15 onc-rupee coins?
A. 14
C. 16
B.15
D. none of these

5. If Dhanvin had one more brother and he had gone through the same process of giving him X one-rupee coins, what could be the smallest number that Dhanvin could have
started?
A. 28
C. 30
B. 29
D.31

Answer 1

Answer:

1. C

2. A

3. D

4. B

5. D

Step-by-step explanation:

You can check answer after solving.

Answer 2

Solution :-

Let initially dhanvin had total N number of coins .

now,

→ Rajiv doubles them = 2N coins .

and,

→ He gave to first brother, Yajvin = x coins .

now,

→ Rajiv doubles left coins again = 2(2N - x) = (4N - 2x) coins .

again,

→ Left coins after giving x coins to his second brother Charan = (4N - 2x) - x = (4N - 3x) coins .

now,

→ Rajiv doubles left coins again = 2(4N - 3x) = (8N - 6x)

again,

→ Left coins after giving x coins to his third brother Reyansh = (8N - 6x) - x = (8N - 7x) coins .

finally, when rajiv doubles left coins they were equal to x .

→ 2(8N - 7x) = x

→ 16N - 14x = x

→ 16N = 15x

now, solving questions :-

1. If Dhanvin started with 30 one-rupee coins, how many did he give to Yajvin?

A. 30

C. 32

B. 31

D. 33

→ N = 30

so,

→ 16 * 30 = 15 * x

→ 16 * 2 = x

→ x(given to yajvin) = 32 (C)

2. What is the minimum number of one-rupee coins could Dhanvin have started with?

A 15

C. 18

B.16

D. 10

for minimum numbers N = 1,

→ 16N = 16 (B)

3. If Dhanvin started with 30 one-rupee coins, what is number of one-rupee coins created (contributed) by Rajeev to all the four brothers?

A. 30

B. 32

C. 128

D.98

when dhanvin started with 30 one rupee coins , N = 30,

→ 16 * 30 = 15x

→ x = 32

then,

→ x coins given to three brothers + 2 extra coins in last to dhanvin = 32 * 3 + 2 = 96 + 2 = 128 (C)

4. What is the maximum possible number contributed by Rajeev, to the X one-rupee coins received by Yajvin, if Dhanvin started with 15 onc-rupee coins?

A. 14

C. 16

B. 15

D. none of these

N = 15,

→ 16 * 15 = 15x

→ x = 16 (C)

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