NIMCET 2017 — Reasoning PYQ

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Question

NIMCET 2017 — Reasoning PYQ

NIMCET | Reasoning | 2017

Three thieves rob a bakery of bread, one after the other, Each thief takes half of what is present and halfa bread . If 3 breads remains at the end , What is the number of breads that were presents initially?

Choose the correct answer:

Explanation

Given:
Remaining bead= 3
Calculation:
Let the initially present bread be the X
First thieve robbery
$\Rightarrow X /2 + 1/2 - - - (1)$
Remaining bread present after 1st robbery
$X - (X/2 +1/2)$
Second thieve rob
$\Rightarrow (X - X /2 - 1/2) /2 + 1/2$
$\Rightarrow (X /2$ -1/2)/2 + 1/2
$\Rightarrow (X - 1) /4$ + 1/2
$\Rightarrow (X + 1) /4$ --(2)
$\Rightarrow X - X /2 - 1/2 - (X + 1) /4$
Third thieve rob
$(X-X/2 -1/2 -(X+1)/4)/2 + 1/2$
On solving above equation we will get
$\Rightarrow (X + 1) /8$ --(3)

Total bread present initially
⇒ X - X/2 - 1/2 - (X + 1)/4 - (X + 1)/8 = 3
⇒ X/2 - X/4 - X/8 = 3 + 1/2 + 1/4 + 1/8
⇒ (4X - 2X - X)/8 = (24 + 4 + 2 + 1)/8
X = 31
∴ The number of breads that were initially presents is 31.