# Free Fractions and Decimals Subjective Test 01 Practice Test - 7th grade

Karan solves a question in 15 seconds. One of his friends challenges him that he can complete the work in one-fourth of the time that Karan takes. What is the time taken by Karan's friend to complete the work? [1 MARK]

#### SOLUTION

Solution :

Time taken by Karan to solve a question= 15 seconds

As per the question,

Time taken by Karan's friend to solve the question
= (1/4) of the time taken by Karan to solve the question
=(15)(1/4) = 3.75 seconds

Hence, Karan's friend will take 3.75 seconds to solve the question.

A bag contains 35 apples and 28 bananas. They are distributed to 7 students such that all have an equal number of apples and bananas. How many fruits does each student get?  [2 MARKS]

#### SOLUTION

Solution :

Concept: 1 Mark
Application: 1 Mark
Given that
Total number of apples = 35

The number of apples each student gets = (35/7) = 5 apples

Total number of bananas = 28

The number of bananas each student gets =(28/7) = 4 bananas

Total number of fruits a student gets = 5 apples + 4 bananas = 9
Hence, each student will get 5 apples and 4 bananas.

Ramesh does 110th of work in an hour while his friend does 110000th of what Ramesh does in the given time. What part of work did Ramesh's friend complete in an hour ? [2 MARKS]

#### SOLUTION

Solution :

Steps: 1 Mark
Answer: 1 Mark

Let the total work be  W

The work completed by Ramesh = 110×W

The work completed by Ramesh's friend = 110×110000W

= 1100000×W

Ramesh's friend completes 1100000th  of the work in the given time,

The area of a rectangle is 50 m2. Find the breadth of the rectangle given that its length is 47m.  [2 MARKS]

#### SOLUTION

Solution :

Formula: 1 Mark
Result: 1 Mark

We know that area of the rectangle =
50m2

Given that the length of the rectangle
= 47
metres

Now, Length × breadth= Area of the rectangle
Let the breadth be 'b' meters

47×b = 50

b = 1752 metres

Hence, the breadth of the rectangle is 1752 metres.

Damayanti ate 29 th part of a pizza. The remaining was divided equally between Hari and Shankar. What part of pizza did Hari and Shankar get?  [2 MARKS]

#### SOLUTION

Solution : Steps: [1 Mark]
Answer: [1 Mark]

Amount of pizza eaten by Damayanti =29

Amount of pizza not eaten by Damayanti

9929=79 This portion is to be divided equally amongst Hari and Shankar. Hari and Shankar will get 79÷21

79×12

718 of the pizza each

So Hari and Shankar each get 718 of the pizza

A man completes a work in 1 hour in his first attempt and in his second attempt he completes it in (1/4) of 1 hour. In his third attempt, he completes it in (4/5)th time of what he took in his second attempt. How long did he take to complete the work in his third attempt? What is the difference in the time taken by him in the first and third attempt?  [3 MARKS]

#### SOLUTION

Solution :

Steps: [1 Marks]
Each answer: [1 Mark]

Time taken by the man in his first attempt = 1 hour

Time taken by the man in his second attempt = 14×1

=  14 hour

Time taken by the man in his third attempt = 14×45

= 15

Hence he took
15 hours to complete the work on his third attempt.

The difference in the time taken by him in his first attempt and third attempt
=115=45 hours

In a match of 50 overs, the team batting second was given a target of 310.They lost the match by 10 runs. The team batting second, i.e. the team which lost, scored one-half of their runs in 30 overs and in next five overs they scored one-half of the remaining runs. Later in the next 8 overs, they scored  15th of the remaining runs. In last seven overs, they scored the remaining runs. How many runs did they score in the last seven overs?
[3 MARKS]

#### SOLUTION

Solution :

Steps: [2 Marks]
Result: [1 Mark]

Total runs scored by the team that lost = 310 - 10 = 300

Now, total no. of overs played by them = 50

i.e. in 30 overs, this team scored =3002

=150 runs

The balance 300 - 150 = 150 runs were scored by this team in balance 20 overs.

By the given condition

In the next 5 overs 12 of 150 runs

= 75 runs were scored.

150 runs - 75 runs = 75 runs are still in balance.

Again in the next 8 overs.

15 of 75 = 15 runs were scored.

Now No. of overs left = 20 - (5 + 8)

=20 - 13
=7 overs

In seven overs, runs scored will be 75 - 15 = 60 runs

A circle is divided into four equal parts. One of the parts is again divided into two equal parts. If the area of the given circle is 400 metre square. What is the area of the shaded region? [3 MARKS]

#### SOLUTION

Solution :

Visualizing the question : 1 Mark
Steps : 1 Mark
Result : 1 Mark Area of the given circle = 400 m2

Area of each sector= 4004=100m2

Area of the shaded portion = 1002
= 50m2

Question 6
Lipika reads a book for 134 hours in a day. If she read the entire book in 6 days how many hours did she take to read the book? In how many days will she be able to complete the book if she would have read for 12 hours each day? [3 Marks]

#### SOLUTION

Solution : Steps: 1 Mark
Calculation: 2 Marks

Time taken by Lipika to read a book =134 hours
She reads the entire book in 6 days.
Now, total number of hours  she took to read the entire book

=134×6=74×6=212=1012 hours

Now if she reads for 12 hours daily, time required by her to complete the book

=1012÷ 12=212÷12=21

Hence, if she reads for half an hour daily she will finish reading the book in 21 days.

The length of the shaded rectangle is (110) of the bigger rectangle and its breadth is 0.001 times the bigger rectangle. If the area of the bigger rectangle is 10000m2. Find the area of the shaded rectangle. [4 MARKS] #### SOLUTION

Solution :

Steps: [3 Marks]
Answer: [1 Mark]

Let the length and breadth of the bigger rectangle be a meters and b meters respectively
As per the question.

The length of the shaded rectangle is (110) of the bigger rectangle.

The length of the shaded rectangle is 0.1×a meters.

The breadth of the shaded rectangle is 0.001 times the bigger rectangle.

The breadth of the shaded rectangle is 0.001×b meters.

Area of the given bigger rectangle =a×b metres =10000m2

Area of the shaded rectangle =(0.1a)×(0.001b)

=(0.0001)×(ab)

=(0.0001)×(10000)

=1 m2
So, the area of the shaded rectangle is 1 m2.

Ram purchased 1.5 kgs of tomato for 35 rupees. If 5.6 kg of tomato is required to prepare 5 kg tomato pickle. What is the cost of 1 kg tomato pickle, given that only tomatoes are used for the preparation of the pickle?  [4 MARKS]

#### SOLUTION

Solution :

Steps: 3 Marks
Result: 1 Mark

Given that
Ram purchased 1.5 kgs of tomato for 35 rupees.

Also, 5.6 kg of tomato is required to prepare 5 kg of tomato pickle.

The first step is to find per kg cost of tomato.

Now, cost of 1 kg of tomato = 351.5 rupees = 35×21.5×2 = 703  rupees

Given that 5.6 kg of tomato is required to prepare 5 kg tomato pickle

Then tomatoes required for making of 1 kg of pickle = 5.65 kgs = 1.12 kgs

Cost of 1kg of tomato pickle =(1.12)×703 = 26.133 rupees

A tap fills one half of a bottle in 1 minute. Three fourth of the remaining in next 1 minute. If the remaining volume is 7m3, then find the volume of the bottle.
[4 MARKS]

#### SOLUTION

Solution :

Steps: [2 Marks]
Application: [1 Mark]
Answer: [1 Mark]
Let the total volume of the bottle be Vm3

Volume filled in the first minute is V2

Volume of the bottle remaining=VV2=V2
Volume filled in the second minute is (34)×(V2) m3

Volume filled in the third minute is V(V2)(34)×(V2)

=(V8) m3

Then the remaining volume    =7 m3

(V8)=7

V=56 m3
The volume of the bottle is 56 m3

A train got derailed and 1114th of the length of the train was found off the track. If the length of the train was 322 m, find out what length of the train was found off the track? What length of the train was still on track?  [4 MARKS]

#### SOLUTION

Solution : Steps: 2 Marks
Answers: 2 Marks Given the length of the train is 322 m

Let x metres be the length that was found off the track. Then using unitary method we have Or, x×1414=322×1114

Or, 14x=322×11

x=322×1114

=32214×11

=23×11

=253 metres

The total length of the train = 322 m
Total length of the train off the track = 253 m
So, the length of the train which was still on track = 322 - 253 = 69 m. Look at the figure above. This is a staircase consisting of 5 steps. The height of each in-step(green area) is 6 cms.

(i) What is the total length of the pink line if the breadth of each step is 32 cms.

(ii) Write the ratio of the height of the instep to its total length of the pink line in the form of a fraction.

[4 MARKS]

#### SOLUTION

Solution : (i) Formula: 1 Mark
Result: 1 Mark
(ii) Formula: 1 Mark
Result: 1 Mark

(i) Given: The height of the staircase = 6 cms

The breadth of the staircase = 32 cms So, length of the pink line will be = (breadth + height) of five steps.
5 (6 cms) + 5 (32 cms)

5[6+32] cms

5 cms

190 cms

(ii) The total length of the instepThe total length of the pink line

5(6) cms190 cms

30190319

Shivaji galloped with his horse for 21 km. He crossed the river which was 13 the length he covered with the horse. He walked the remaining distance which was 4 times the breadth of the river.
Calculate the total distance covered by him.  [4 MARKS]

#### SOLUTION

Solution : Concept: 1 Mark
Steps: 2 Marks
Result: 1 Mark The breadth of the river =13×21

=7 km

Length covered by walking =4(13 of 21) km

4(7 km)

28km

Hence, the total distance covered by Shivaji = 21km + 7km + 28km

28km + 28km
= 56km

The total distance covered by Shivaji is 56km.