Question

IAS question - ❓❓❓❓❓❓

A man starts frm his house with some money to visit four temples.

1. As soon as he enters temple 1 his money gets doubled. He donates 100 rs nd moves.

2. At temple 2 again his money is doubled and he donates 100 rs.

3. His money is doubled again at temple 3 and he donates 100 rs.

4. At temple 4 again his money gets doubled. He donates 100 rs. again
and
returns home empty handed.

How much money he had when he started from his house???

This is a challenge for all the masterminds...

lets see who cracks .

❓❓❓❓❓❓❓​

Answer 1

Answer:

The man started with Rs. 93.75

Step-by-step explanation:

Given :

Every time he enters a temple, the money gets doubled and he donates Rs. 100 from it.

At the end, the man doesn't have any money

To find :

Amount he started with

Solution :

Consider the amount which man started with as y

• Temple 1 -

Money gets doubled = 2 × y = 2y

Rs. 100 donated = (-100)

⇒ 2y - 100 ---- (Temple 1)

$\rule{300}{1.5}$

With the amount he got from Temple 1, he goes to Temple 2,

• Temple 2 -

Money gets doubled = 2(2y - 100)

Rs. 100 donated = (-100)

⇒ 2(2y - 100) - 100

⇒ 4y - 200 - 100

⇒ 4y - 300 ---- (Temple 2)

$\rule{300}{1.5}$

• Temple 3 -

Money gets doubled = 2(4y - 300)

Rs. 100 donated = (-100)

⇒ 2(4y - 300) - 100

⇒ 8y - 600 - 100

⇒ 8y - 700 ---- (Temple 3)

$\rule{300}{1.5}$

• Temple 4 -

Money gets doubled = 2(8y - 700)

Rs. 100 donated = (-100)

⇒ 2(8y - 700) - 100

⇒ 16y - 1400 - 100

⇒ 16y - 1500 ---- (Temple 4)

$\rule{300}{1.5}$

According to the question,

Man has Rs. 0 when he returns back home.

⇒ Amount from temple 4 = 0

⇒ 16y - 1500 = 0

⇒ 16y = 1500

⇒ y = 1500/16

⇒ y = 93.75

Amount he started with = Rs. 93.75

$\therefore$ The man started with Rs. 93.75

Answer 2

$\sf{\underline{\underline{Answer : }}}$

Let the amount the man initially had be x

When he reached the first temple, the money doubled. So, the amount now is 2x.

He donates 100. So, balance amount = 2x – 100

This again doubles at 2nd temple. So, he has 2 (2x - 100) => 4x – 200

He gives 100. So, he has 4x – 200 – 100 = 4x – 300

Same process at Temple 3.

It doubles and he has 2(4x - 300) = 8x – 600

He gives 100. So, he has 8x – 700

Again doubling at Temple 4. Thus, he has 2(8x - 700) = 16x – 1400

He gives 100 and has nothing. Thus 16x – 1400 – 100 = 0

=> 16x – 1500 = 0

=> 16x = 1500

Therefore, x = 1500/16 = 93.75

Thus, he started from home with Rs.93.75