Question

A person has to meet a king for that he has to cross 7 gates Al each gate he has to pay half the amount he is carrying Finally he gave Rs 3 to the king Then the amount he carried at the beginning A 344 B 342 BC

Answer 1

Answer:

A person has to meet a king for that he has to cross 7 gates Al each gate he has to pay half the amount he is carrying Finally he gave Rs 3 to the king Then the amount he carried at the beginning is Rs 384

Step-by-step explanation:

Let x be the initial amount of money the man was carrying before crossing the seven gates.

At each gate he pays half the amount he is carrying.

We analyze this as follows:

• The first gate: 1/2 x remains
• The second gate: 1/2 × 1/2x = 1/4x
• The third gate: 1/2 × 1/4x = 1/8x
• The fourth gate: 1/2 × 1/8x = 1/16x
• The fifth gate: 1/2 × 1/16x = 1/32x
• The sixth gate: 1/2 × 1/32x = 1/64x
• The seventh gate: 1/2 × 1/64x = 1/128x

Since he gave what was left at the seventh gate we have:

1/128x = 3

So x is given by:

x = 3 × 128 = 384

So at the beginning he had Rs 384