Question

the owner of a local jewellery store hired 3 watchmen to guard his diamonds but a thief still got in and stole some diamonds. on the way out the thief met each watchman one at a time. to each he gave 1/2 of the diamonds had then and 2 more besides. he escaped with one diamond. how many did he steel originally?

Answer 1

Let the total number of diamonds be x then :

To watchman one the thief gives :

= 1/2x + 2

Remaining : x - 1/2x - 2= 1/2x - 2

To watchman two the thief gives :

1/2(1/2x - 2) = 1/4x - 1 + 2 = 1/4 x + 1

Remaining : 1/2x - 2 - 1/4x - 1 = 1/4x - 3

To watchman 3:

= 1/2(1/4x - 3) + 2 = 1/8x - 1.5 + 2 = 1/8x + 0.5

Remaining : 1/4x - 3 - 1/8x - 0.5 = 1/8x - 3.5

1/8x - 3.5 = 1

1/8x = 4.5

x = 4.5 × 8

x = 36

There were 36 diamonds.

Answer 2

Answer:

Let the no of diamond be 16x

1st thief = 8x+2

remaining = 8x-2

2nd thief = 4x-1+2=4x+1

remaining= 4x-3

3rd thief= 4x-3/2 +2= 4x+1/2

remaining= 4x-3 -4x+1/2 = 4x-7/2

and finally, 4x-7/2= 1

x= 9/4

:16x= 36