**8th grade math worksheet 5 answer :**

Here we are going to see 10 practice questions of mixed topics. We have been preparing this set of questions in order to test how you understood the topics.

**Question 1 :**

Find the value of x in 12 : 16 :: x : 20

(A) 14 (B) 14 (C) 15

**Solution :**

Since the given two ratios are in proportion, we have to equate the ratios.

(12 / 16) = (x / 20)

x = 12 (20)/16

x = 3(5)

= 15

Hence the value of x is 15.

**Question 2 :**

A fort had enough food for 120 soldiers for 200 days. After 5 days 30 soldiers leave the fort. How long will the remaining food last now?

(A) 260 days (B) 140 days (C) 120 days

**Solution :**

Provision available for 120 men for 200 days .

total provision can be consumed by 1 man = 120 × 200 = 24000 days .

Since , after 5 days 30 men left

Total provision consumed in 5 days= 120 × 5 = 600 men days

total provision left = 24000 - 600 = 23400 men days

Persons left after 5 days = 120 - 30 = 90 men

No of days it can last for remaining people = 23400/90 = 260 days

Thus, the remaining provision will last for 260 days.

**Question 3 :**

If a scooter travels 155 km on 5 liters of petrol, how many kilometers will it travel on 9 liters of petrol ?

(A) 139 km (B) 279 km (C) 100 km

**Solution :**

Distance traveled by the scooter by consuming 5 liters of petrol = 155 km

Distance traveled by consuming 1 liter of petrol = 155/5

= 31 km

Number of km traveled by the scooter by consuming 9 liters of petrol = 31 **⋅** 9

= 279 km

**Question 4 :**

If 20 men can build a wall 112 meters long in 6 days, what length of a similar wall can be built by 25 men in 3 days?

(A) 80 meters (B) 70 meters (C) 20 meters

**Solution :**

**Step 1 :**

Consider the number of men and the length of the wall. As the number of men increases from 20 to 25, the length of the wall also increases. So it is in Direct Variation.

So, the proportion is 20 : 25 :: 112 : x ...... (1)

**Step 2 :**

Consider the number of days and the length of the wall. As the number of days decreases from 6 to 3, the length of the wall also decreases. So, it is in Direct Variation.

So, the proportion is 6 : 3 :: 112 : x ..... (2)

Combining (1) and (2), we can write

20 **⋅** 6 **⋅ x **= 25 **⋅** 3 **⋅** 112

x = (25 **⋅** 3 **⋅** 112) / (20 **⋅** 6)

x = 70 meter

**Question 5 :**

ABCD is a parallelogram in which angle of DAB and DBC 75°, 60° respectively. Calculate the angles CDB and ADB.

(A) 49°, 51° (B) 45°, 60° (C) 21°, 75°

**Solution :**

<DAB + <ADC = 180

75 + <ADC = 180

<ADC = 180 - 75 = 65°

<ADC = <ADB + <BDC -----(1)

105 = 60 + <BDC

105 - 60 = <BDC

<BDC = 45°

<ADB = 60° (Alternate angles)

Hence the required angles are 45° and 60°

**Question 6 :**

If the selling price of 10 articles is equal to the cost price of 11 articles.Find the profit percent.

(A) 15% (B) 10% (C) 12%

**Solution :**

Now we calculate the cost price of 9 articles.

Cost price of 9 articles = 1 x 9 = $ 9

Thus,

Profit made on the selling of 9 articles

= Selling price of 9 articles - Cost price of 9 articles

Profit made on the selling of 9 articles = 10 - 9

Profit made on the selling of 9 articles = $ 1

% Profit or % Gain = ( Profit / Cost Price ) x 100 %

% Gain = ( 1 / 9 ) x 100 %

% Gain = 11.11 %

Hence the answer is 12%

Let us look into the solution of next problem on "8th grade math worksheet 5 answer"

**Question 7 :**

Find AC when AB = 15 cm, AD = 10 cm, AE = 8 cm

(A) 12 cm (B) 10 cm (C) 13 cm

**Solution :**

DE || BC

AD / DB = AE / EC ------(1)

AB = 15 cm

AD + DB = 15

10 + DB = 15

DB = 15 - 10 = 5 cm

AD = 10 cm, AE = 8 cm

Applying these values in the first equation, we get

10 / 5 = 8 / EC

EC = 8 (5) / 10

EC = 4 cm

AC = AE + EC ==> 8 + 4 = 12 cm

Hence the length of AC is 12 cm.

Let us look into the solution of next problem on "8th grade math worksheet 5 answer"

**Question 8 :**

Angle ABC measures 250°, find the measure of minor of arc AC.

(A) 150° (B) 110° (C) 140°

**Solution :**

<ACB = 360 - 250

= 110°

Hence the required angle is 110°.

Let us look into the solution of next problem on "8th grade math worksheet 5 answer"

**Question 9 :**

Find the mean of all odd numbers between 80 and 88.

(A) 84 (B) 30 (C) 62

**Solution :**

To find the mean of odd numbers between 80 and 88.

let us list out the numbers between 80 and 88.

81, 82, 83, 84, 85, 86, 87

Odd numbers are 81, 83, 85 and 87.

Mean = (81 + 83 + 85 + 87)/4

= 336/4

= 84

**Question 10 :**

The number of times a particular observation occur in a data is called its __________

(A) Frequency (B) Mean (C) Median

**Solution :**

The number of times a particular observation occur in a data is called its frequency.

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