# Question 57 & 58

(Federal Public Service Commission AD Intelligence Bureau Screening Test 2018)

Solution:

**Description:**

We use here our common sense to solve this question. i-e one cut will always give two pieces, (one number more than cut number) – is the start point! so 9 cuts will give 10 pieces. Then we will use unitary method to find the solution.And in this way the solution will be found!

**Statrt:**

Clearly one cut will divide the roll in two parts as shown in figure below:

*i-e we can say 1 cut = 2 pieces and 2 cuts =3 pieces ……………9 cuts =10 pieces and so on!*

So if the tailor cuts a roll into 10 pieces, then he will have to make 9 cuts!

It is given also that he can make 45 cuts in 1 minute:

So, in 24 minutes he will make 45×24= 1080 cuts!

It is also given that 1 roll takes 9 cuts of shirt pieces;

i-e

(i

(Above can be explained by saying that 9 cuts are equal to one roll – then divide both sides by 9, we get this equation saying 1 cut is equale to 1 over 9 rolls. Multiply both sides with 1080, then we get 1080 cuts equal to 120 rolls i-e 120 rolls will give us 1080 made in 24 minutes)

**So, The tailor will cut 120 rolls in 24 minutes!**

(Federal Public Service Commission AD Intelligence Bureau Screening Test 2018)

Solution:

**Description:**

Here we will make two equations by given conditions,

Then we will equate one variable to relation of two others.

Then equating both equations we will find relation in other two variables

Start:

Here we are given that A is 3 year older to B i-e to make A and B of equal age, we will subtract 3 years from A’s age;

i-e A-3 =B

or A=B+3 —-(1)

Also, A is 3 years younger to C i-e to make A and C of equal age, we will have to add 3 years to A’s age

i-e A+3=C

or A=C-3 — (2)

From equation 1 & 2 we can write;

B+3=C-3

Or

C-B=6 ——(3)

But B and D are twins, i-e both are of equal age ! i-e B=D, put in eq 3

C-D=6

or C=D+6

**Or it means that C and D will become of equal age if 6 years are added to the age of D i-e C is 6 years older to D**