Grade 7 Ratio Proportion and Variation Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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(1) Two Ratio X: Y and Y: Z Are Given. Write X: Y: Z

(a)

(b)

(c)

(2) Answer the Following

(a) Vicky՚s and Rocky՚s age are in ration 3: 2. Five year ago, their ages were in the ratio 5: 3, what are their present ages?

(3) Answer the Following

(a) Mahesh have ₹ 8960 in his wallet. From them twenty rupees, fifty rupees and two hundred rupees notes are in the ratio 9: 6: 4. How many twenty rupees note does Mahesh have?

(4) Write in “D” if Y and X Very Directly and “I” if They Very Inversely

(a)

Illustration 2 for 4Write_in_D_if_y_and_x_very_dir …

(b)

Illustration 3 for 4Write_in_D_if_y_and_x_very_dir …

(5) Fill in the Boxes After Identifying the Constant of Proportionality

(Note: Y ∝ X)

(a)

Table Supporting: 5_Fill_in_the_boxes_after_identifying_the_constant_of_proportionality
X630728
y89612430

(6) Fill in the Boxes After Identifying the Constant of Proportionality

(Note: Y ∝ X)

(a)

Table Supporting: 6_Fill_in_the_boxes_after_identifying_the_constant_of_proportionality
X4921357014
y561616

(7) if 9 Mobile Cost ₹ 54000, if “N” in the Number of Mobile and “T” is Total Cost of Mobile Then

(a) T is ________ proportional to n

(b) Fill in the table with correct value.

Table Supporting: 7_if_9_mobile_cost_Rs_54000_if_n_in_the_number_of_mobile_and_T_is_total_cost_of_mobile_then
n310
T (₹)30,00072000

(8) a Four Wheel Running at a Speed of 39 Km/H and Cross a Bridge in 20 Minute. What is the Length of the Bridge?

(9) a Cargo-202 Flight Flies at 290 Km/H. How Long Will It Take to Fly 98600km?

(10) Vikas Was Going for Picnic, He Drive His Car at a Speed of 55 Km/H for 2 Hours Than 40 Km/H for 3 Hours and then 60km/H for 1 Hour. What is His Average Speed for the Whole Journey?

(11) when Class Was Ended a Student Was Left the Class by His Motor Cycle and His Speed is 40 Km/H After 45 Minutes Sir Left the Class by His Four Wheel and Speed of His Four Wheel is 60 Km/H at What Distance Will They Meet if They Were in Same Route?

(12) Production House Can Manufacture a 50 Cutting Machine in 90 Days How Many Days Will It՚s Take to Manufacture 20 Cutting Machine

(13) Science College Has 6 Period a Day, with Each Period 1hour 30 Minute Long. How Long Would Each Period be if the School Had 9 Period Instead of 6? (College Timing Don՚t Change)

(14) 16 Man Can Complete Digging Work in 5 Days

(a) How long will 12 man take to complete the job?

(b) How many man will be needed to complete the digging work in 5 days?

(15) 7 Taps Can Empty Water Tank in 20 Hours

(a) How many taps are needed to empty the water tank in 28 hours?

(b) How much time will 10 taps take to empty the water tank?

Answers and Explanations

Answer 1 (A)

  • Given
  • To find , Value of y should be same in both ration
  • If we multiply by 4 to the denominator and numerator of ratio than value of y will be same in both ratio.

  • And given that
  • Now value of y is same in both the ratio
  • So y can be eliminated/both ratio can be marge as below,

Answer 1 (B)

  • Given
  • Here y is common in both the ratio therefore,
  • To find , Value of y should be same in both ration
  • If we divide by 3 to the denominator and numerator of ratio than value of y will be same in both ratio.

  • And given that
  • Now value of y is same in both the ratio
  • So y can be eliminated/both ratio can be marge as below,

Answer 1 (C)

  • Given
  • Here y is common in both the ratio therefore,
  • To find , Value of y should be same in both ration
  • If we multiply by 8 to the denominator and numerator of ratio than value of y will be same in both ratio.

  • And given that
  • Now value of y is same in both the ratio
  • So y can be eliminated/both ratio can be marge as below,

Answer 2 (A)

  • Vicky՚s and Rocky՚s age are in ration 3: 2.
  • Suppose Vicky՚s age is x; and Rocky՚s age is y.
  • Now given that ratio so their age is
  • So,

  • Five year ago, their ages were in the ratio 5: 3
  • So,

  • Put the value of

  • Therefore Vicky՚s and Rocky՚s age are 30 years and 20 years respectively.

Answer 3 (A)

  • Mahesh have ₹ 8960 in his wallet
  • He has only twenty rupees, fifty rupees and two hundred rupees notes are there in his wallet and the ratio of
  • And the ratio of twenty rupees, fifty rupees and two hundred rupees notes are 9: 6: 4
  • Suppose he has x number of notes with respect to ratio in his wallet so ,

  • So, Mahesh has

Answer 4 (A)

  • Given table for the value of x and y is as below,
Table Supporting: Answers_and_Explanations
X612607112030
y816809616040
  • From table it can be seen that as the value of x increase from 6 to 12 to 60 to 71 … . etc. The value of y also increase from 8 to 16 to 96 to 160 to 40.
  • That means y is directly proportional to x; means as the value of x increase , value of y increase.
  • So,
Illustration 4 for Answers_and_Explanations

Answer 4 (B)

  • Given table for the value of x and y is as below,
Table Supporting: Answers_and_Explanations
X45403026188
y458122430
  • From table it can be seen that as the value of x decrease from 45 to 40 to 30 to 26 … ; the value of y increase from 4 to 5 to 8 to 12 …
  • That means x is inversely proportional to y; means as the value of y increase , value of x decrease.
  • So ,
Illustration 5 for Answers_and_Explanations

Answer 5 (A)

  • Given table for the value of x and y is as below,
Table Supporting: Answers_and_Explanations
X630728
y89612430
  • From table;

  • Compare this
  • Than proportionality constant

  • When

  • When

  • When

  • So, complete table is as below
Table Supporting: Answers_and_Explanations
X63072938
y8409612430

Answer 6 (A)

  • Given Table for the value of x and y is as below,
Table Supporting: Answers_and_Explanations
X4921357014
y561616
  • From table;

  • Compare this
  • Than proportionality constant

  • When

  • When

  • When

  • When

  • So, complete table is as below,
Table Supporting: Answers_and_Explanations
X492114357014
y562416408016

Answer 7 (A)

  • Cost of 9 mobile is ₹ 54000.
  • And for the cost, as the number of mobile (n) increase final cost (T) also increase
  • So T is directly proportional to n,

Answer 7 (B)

  • Cost of 9 mobile is ₹ 54000.
  • So,

  • Now given table that,
Table Supporting: Answers_and_Explanations
n310
T (₹)30,00072000
  • When

  • When

  • When

  • When

  • So, Complete Table is given below,
Table Supporting: Answers_and_Explanations
n351012
T (₹)1800030,00060,00072000

Answer (8)

  • Four wheel running at a speed 39 Km/h.
  • So. In one hour four wheel travel 39 Km.
  • If we consider time (T) and distance (D) then

  • When

  • So, length of bridge is 13 km

Answer (9)

  • A cargo flight flies at speed at 290 Km/h.
  • Means in one hour flight can travel 290 Km.
  • If we consider time (T) and distance (D) then

  • When D is 98600 Km.
  • Then,

  • So, Flight will take 340 hours to travel 98600 Km.

Answer (10)

  • Vikas drive his car at speed of 55km/h for 2 hours.
  • Then 40 km/h for 3 hours.
  • Then 60 km/h for one hour.
  • So,

  • So, average speed of vikas during his whole journey is 25.83 km/h

Answer (11)

  • Speed of motor cycle of Student is
  • Means in one hour he can travel
  • Now,

Illustration 6 for Answers_and_Explanations
  • In Above figure point A is class.
  • In 45 minute student reach at point B. and then sir stated to travel from class (Point A)
  • Now suppose they meet at Point C.
  • And suppose distance of Point C from Point B is
  • So, Student have to travel and sir have to travel
  • Now suppose they meet after time (t) then,
  • For Student

  • For Sir,

  • So, Distance of Point C from Point B is
  • So, they will meet at from class.

Answer (12)

  • Production house can manufacture a 50 cutting machine in 90 days.
  • If we take cutting machine as (M) and time taken to manufacture that much machine in (d) then,

  • Now when

  • So, it will take 36 days to manufacture 20 machine.

Answer (13)

  • Science College has 6 period a day, with each period 1hour 30 minute long.
  • So, college time is

Now if number of period changed from 6 to 9 and also college time will remain same then in that case,

  • Therefore if number of period changed from 6 to 9 and college time will remain same than duration of period will change to one hour.
  • So, New duration of each period is ONE HOUR

Answer 14 (A)

  • 16 man can complete digging work in 5 days.
  • If we consider number of people required for digging work in “n” and number of days they work in “d” the,

  • When number of people working for digging is 12 (n = 12) ,

  • So, 12 people can complete digging work in

Answer 14 (B)

  • 16 man can complete digging work in 5 days.
  • If we consider number of people required for digging work in “n” and number of days they work in “d” the,

  • If work should complete in 5 days then,

  • So, 16 people required to complete digging work in 5 days.

Answer 15 (A)

  • 7 Taps can empty the water tank in 20 hours.
  • If we consider number of taps in “n” and number of hour taken by them to empty the water tank in “h” then,

  • Because as the number of taps increase water tank will empty soon; means they are in inversely proportion.

  • 7 Taps can empty the water tank in 20 hours. Means

  • So,

  • Now if need to empty water tank in 28 hours then

  • So, 5 taps required to empty water tank in 28 hours.

Answer 15 (B)

  • If 10 taps install to empty the water tank then,

  • So, 10 number of taps can empty water tank in 14 hours.

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