__Question no 6 (a):__

__Question no 6 (a):__

**Moiz was trying to sleep at one night but there was too much noise around him. His clock ticked every 5 second: a tap was dipping every 7 second and a pet dog snored every 12 second. He noticed on his clock that all three things happened together on the stroke of mid night. Find after how many seconds all three things happened together again?**

__Solution:__

__Solution:__

Calculate least common multiple for 12, 5 and 7

Factorize the above numbers

Prime factor of 12 = 2 *x* 2 *x* 3 *x* 1

Prime factor of 5 = 5 *x* 1

Prime factor of 7 = 7 *x* 1

LCM = common factors *x* uncommon factors

LCM = 1 *x 2 x 2 x 3 x 5 x 7 *

LCM = 420

At midnight all three noises come together, then all three noises come together after 420 seconds**.**

__Question no 6: (b)__

__Question no 6: (b)__

**One pipe can fill a pool 1.25 times as fast as a second pipe. When both pipes are opened, they fill the pool in five hours. How long would it take to fill the pool if only the slower pipe is used?**

__Solution:__

__Solution:__

Let’s assume the rate of slower pipe =X

So, the rate of faster pipe would be = 1.25X

Working together , their rate will be= X + 1.25X

According to question , working together they take 5 hours to fill up the tank , So:

Rate x time = work

2.25X *x* 5 = 1

2.25X = 1/5

X = 1/5 *x* 1/2.25 = 4/45

So , the rate of slower pipe , X = 4/45

Now, let’s see how long it takes for the slower pipe to complete the task :

Rate *x* time = work

4/45 *x* time = 1

Time = 1 *x *45/4 = 45/4 = 11.25

__Question no 6 (c) :__

__Question no 6 (c) :__

**The cost for hiring a car for 2 days in 2018 was Rs 264 which was 20% more than in 2013. What was the cost of hiring a car for 2 days in 2013?**

__Solution:__

__Solution:__

Suppose in 2013 the expenditures were = X

In 2018 the expenditures with the increase of 20 percent of X were = 264

Now, according to given condition the equation will become

X + 20% of X = 264

X + 20X/100 = 264

By taking LCM

100X + 20X /100 = 264

120X / 100 = 264

X = 264 *x* 100/120

X = 26400/120

X = 220

Hence in 2013 the expenditures were Rs. 220

__Question no 6 (d): __

__Question no 6 (d):__

**What do you understand by measure of central tendency? State its types.**

__Solution:__

__Solution:__

**Definition of Central Tendency**:

A measure of central tendency is a summary measure that attempts to describe a whole set of data with a single value that represents the middle or center of its distribution.

There are three main measures of central tendency:

- Mean
- Median
- Mode

Each of these measures describe the central value.

__Mean:__

Sum of value of each observation/data is divided by the total of observation is called mean.

Mean = sum of all observation/total of observation

For example

Data = 3,4,5,6,7

Mean = 3 + 4 + 5 + 6 +7 /5

Mean = 25 /5 = 5

So, Mean is 5

__Median:__

Middle value of the observation/data is called median

To calculate median first you must arrange the data/observation in ascending and descending order.

For example

Data: 3,4,5,6,7

mid value is 5

it means 5 is the median

__Mode:__

Most repeated value in the observation/data is called mode.

For example

Data = 3 ,3 , 4 , 5, 6,6,6, 7, 7, 8

most repeated value is 6

it means 6 is the mode.

**Question no 7 (a):**

**Moiz and Mair share a lottery win of Rs 2000 in the ratio 1:4. Moiz then share his part between himself, his wife and their son in the ratio 4:5:1. How much does his wife get over their son.**

**Solution:**

Total distributed amount = 2000

Ratio between Moiz and Maire = 1:4

Sum of ratio = 1 + 4 = 5

Moiz = 1/5 *x *2000

Moiz = 400

Now the amount Rs. 400 is distributed among Moiz, his wife and son with the ratio 4:5:1

The sum of ratio = 4 + 5 + 1 = 10

Now, Moiz will get = 4/10 *x *400 = 160

Then wife will get = 5/10 *x *400 = 200

And son will get = 1/10 *x *400 = 40

Difference of wife and son money = 200 – 40 = 160

Hence, his wife will get 160 more than his son.

**Question no 7 (b):**

**A farmer keeps hens and rabbits on his farm. One day, he counted a total of 70 heads and 196 legs. How many more hens than rabbits does he have?**

**Solution:**

Let the number of hens = X

The number of rabbits = y

According to condition

X + Y = 70 ———– equation 1

2X + 4Y = 196 ———- equation 2

Solving equation 1,

Subtracting X on both sides

X – X + Y =70 – X

Y = 70 – X equation 3 (put in equation 2)

2X + 4(70 – X) = 196

2X + 280 – 4X = 196

-2x + 280 = 196

-2x = 196-280

-2x = -84

X = 42 put in equation 3

Y = 70 – 42

Y = 28

Hence hens = 42

Rabbits = 28

Difference = hens – rabbits = 42-28 = 14

Hence there are 14 hens more than rabbits.

**Question no 7 (c):**

**What is polygon? Describe different types of regular polygon.**

**Solution:**

**Polygon:**

A many-sided figure is called polygon.

**Types of Polygon:**

There are different types of regular polygon.

**Triangle**

Three-sided figure is called triangle having three interior angles

**Quadrilateral**

A four-sided figure is called quadrilateral having 4 interior angles.

**Pentagon**

A five-sided figure is called pentagon having 5 interior angles.

**Hexagon**

A six-sided figure is called hexagon having six interior angles.

**Heptagon**

A seven-sided figure is called heptagon having 7 interior angles

**Octagon**

An eight-sided figure is called octagon having 8 interior angles.

**Nonagon**

A nine-sided figure is called decagon having nine interior angles.

**Decagon**

A ten-sided figure is called decagon having 10 interior angles.

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**Question no 7 (d):**

**In a certain code, computer is written as RFUVQNPC. How will MEDICINE be written in code language?**

**Solution:**

COMPUTER————————-RFUVQNPC

MEDICINE ————————– EOJDJEFM

**Explanation:**

If we compare the words COMPUTER and RFUVQNPC, we see that from the word computer all alphabets are written consecutively in the word RFUVQNPC and R in the beginning and C at the end.

Just like that

Write the reverse of word COMPUTER

R | E | T | U | P | M | O | C |

R | F | U | V | Q | N | P | C |

Similarly, we solve MEDICINE same as the word COMPUTER is solved.

We write the reverse of word MEDICINE

E | N | I | C | I | D | E | M |

E | O | J | D | J | E | F | M |

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**Question no 8 (a):**

**Seven piano students- T, U, V, W, X, Y and Z- are given a recital and their instructor is deciding the order in which they will perform.**

**Each student will play exactly one piece, a piano solo. In deciding the order of performances, the instructor must observe the following restrictions:**

**1. X cannot play first or second**

W cannot play until X has played

Neither T nor Y can play seventh.

Either Y or Z must play immediately after W plays

V must play immediately after or immediately before U plays

**2.If V plays first, which one of the following must be true**

T plays sixth

X plays third

Z plays seventh

T plays immediately after Y

W plays immediately after X

**Solution:**

**(1)**

According to condition the order will be as follows

V, U, T, X, W, Y, Z

(2**)**

If V plays first, then

Z plays seventh

**Question no 8: (b)**

**U = { whole number from 10 to 24}**

**A = { Even number}**

**B = { number divisible by 5}**

**Write down the number of elements of ****A****∩B.**

**Solution:**

U = { 10,11,12,13,14,15,16,17,18,19,20,21,22,23,24}

A = { 0,2,4,6,8,10,12, ……}

B = {5,10,15,20,25,30,35,40, …….}

A∩B = { 10,20,30,40,50, ……}

**Question no 8: (c)**

**In the following diagram A represent American, S represent Scientists and P represent Politicians.**

**American those are politicians but not scientists will be?****Scientists which are politicians but not Americans will be?**

**Solution:**

- C, b and g is the answer
- e, f and g are the answer

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**Question no 8: (d)**

**Each packet of washing powder carries a token and 4 tokens can be exchanged for free packet. How many free packets will I receive if I buy 64 packets?**

**Solution:**

One packet contains = one token

64 packets contain = 64 tokens

No of free packets= 64 / 4 = 16 packets

We receive 16 packets in exchange of 64 packets

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