During revision, students quickly go through Class 7 Maths Extra Questions Part 2 Chapter 7 Finding the Unknown Class 7 Extra Questions with Answers for clarity.
Class 7 Finding the Unknown Extra Questions
Class 7 Maths Chapter 7 Finding the Unknown Extra Questions
Finding the Unknown Extra Questions Class 7
Question 1.
The sum of a number and 15 is 35. Find the number.
Solution:
Let the number be x. Then,
x+15=35 ⇒ x=35-15 ⇒ x=20
So, the number is 20
Question 2.
Subtracting 9 from twice a number gives 25. Find the number.
Solution:
Let the number be x. Then,
2 x-9 = 25 ⇒ 2 x=25+9
⇒ 2 x =34 ⇒ x=17
Question 3.
The perimeter of a rectangle is 48 cm. If its length is 3 cm more than twice its breadth, find its length and breadth.
Solution:
Let breadth (b)=x cm
Then length (l)=2 x+3cm
Perimeter =2(l+b)
⇒ 2(2 x+3+x) =48
⇒ 6 x+6 =48 ⇒ 2(3 x+3)=48
⇒ x =\(\frac{42}{6}\) = 7cm
2 x+3 =2(7)+3=17 cm
So, length =17cm and breadth =7 cm.
Question 4.
Three consecutive integers add up to 84. Find the integers.
Solution:
Let the first integer be x.
Then the next two are (x+1) and (x+2).
According to question,
x+(x+1)+(x+2)=84 ⇒ 3 x+3=84
⇒ 3x=81 ⇒ x=27
Hence, the integers are 27, 28, and 29.
Question 5.
Solve these equations.
(a) -2(m-5)=3(m+1)
(b) 12-4 a=2(a-3)-(a-6)
Solution:
(a)-2(m-5)=3(m+1) ⇒ -2 m+10=3 m+3
⇒5 m=7 ⇒ m=\(\frac{7}{5}\)
(b) 12-4 a =2(a-3)-(a-6)
⇒ 12-4 a =2 a-6-a+6
⇒ 5a =12 ⇒ a=\(\frac{12}{5}\)
Question 6.
Rani’s mother is three times as old as Rani. After 12 years, her mother will be twice Rani’s age. Find their present ages.
Solution:
Let Rani’s age be x years.
Then mother’s age = 3 x years.
After 12 years:
Mother’s age = 3 x+12, and Rani’s age =x+12
According to question,
3 x+12 =2(x+12) ⇒ 3 x+12=2 x+24
x =12
Rani’s age =12 years, Mother’s age =3 × 12=36 years
Question 7.
The denominator of a fraction is 4 more than its numerator. If the fraction equals \(\frac{3}{7}\), find the fraction.
Solution:
Let the numerator be x.
Then denominator =x+4.
So, \(\frac{x}{(x+4)} =\frac{3}{7}\) ⇒ 7 x=3(x+4)
7 x =3 x+12 ⇒ 4 x=12
x =3
Numerator =3, Denominator =3+4=7.
∴ The fraction is \(\frac{3}{7}\).
Question 8.
Find the step in the sequence when 128 tiles are arranged in the given arrangement.
Solution:
We note that 1 tile is added to left, right and the tail to get next step arrangement. Thus the pattern is 3 x+2 where x is the no. of step.
3 x+2 tiles are in xth step.
Let 128 tiles be the steps of nth pattern
3n+2=128
Transposing 2
3n =128-2
⇒ 3n =126
Transposing 3
n=126 ÷ 3
n=42
In 42nd step tiles used will be 128.
Question 9.
Taxi fare comprises of fixed charge of ₹ 40 and an additional charge of ₹ 12 per kilometer. Ramdeen paid ₹ 100 while going from his office to market. How far is his office from market?
Solution:
Let distance from office to market be x km
Charge for covering x km is ₹ 12 x.
According to question,
₹ 40 + ₹ 12x = ₹ 100
⇒ 40+12 x=100
Transposing +40 to R.H.S.
12 x =100-40
⇒ 12 x =60
Transposing 12 to R.H.S.
x=60 ÷ 12
x=5
∴ Distance from office to market =5 km
Question 10.
A private library offers monthly membership of ₹ 200. The library charges ₹10 for first 3 days and ₹ 4 per day thereafter for every book issued.
Rajni paid ₹ 240 for the month of July. She had borrowed two books from the library and returned one of the book on the third day but kept the other book a little longer.
For how many days did she keep the second book?
Solution:
Monthly membership of charge =₹ 200
As one book was returned on the third day so Rajni paid only ₹ 10 for this book.
Let no. of additional days she kept the second book be x (days).
So charges to be paid for second book
=₹ 10+₹ 4 × x
Total money paid by Rajni =₹ 240
According to question,
₹ 200+₹ 10+₹(10+4 x)=₹ 240
⇒ 200+10+10+4 x=240
⇒ 220+4 x=240
Transpose 220
4 x=240-220
4 x=20
Transpose 4
x =20÷4
⇒ x =5
Rajni kept the book for 5 additional days.
No. of days for which the second book was with Rajni =3+5=8 days
Question 11.
Riddhi and Vriddhi have equal no. of toffees. Riddhi gave 5 toffees to Vriddhi. Now Vriddhi has twice as many toffees as Riddhi. How many toffees did each one have initially.
Solution:
Let Riddhi and Vriddhi have x toffees in the beginning.
After Riddhi gave 5 toffees to Vriddhi
Riddhi has x-5 toffees
Vriddhi has x+5 toffees.
According to question
x+5=2(x-5)
x+5=2 x-10
Transposing 2 x to LHS
x+5-2 x=-10
-x+5=-10
Transposing 5 to RHS
-x =-10-5
⇒ -x =-15
⇒ x =15
Riddhi and Vriddhi both have 15 toffees initially.
Solving linear equations in different ways.
Question 12.
Solve for x : 4(x-5)=12
Solution:
Method 1
4(x-5)=12 (Using Distributive Property)
4 x-20=12
Transpose -20
⇒ 4 x=12+20
⇒ 4 x=32
Transpose 4
⇒ x=32 ÷ 4
⇒ x=8
Method 2
4(x-5)=12
Transpose 4
⇒ (x-5)=12 ÷ 4
⇒ x-5=3
Transpose -5
⇒ x=3+5
⇒ x=8
Question 13.
Can you give a real life situation that can be modelled as 15 x+20=80.
Solution:
Ramesh pays ₹ 80 to the delivery boy including delivery charges for a certain quantity of onions. If the delivery charges are ₹ 20 and rate of onions is ₹ 15 per kg, what is the quantity of onions bought.
OR
Arjun has 20 marbles more than five times marbles Bheem has. If Arjun has 80 marbles, how many marbles does Bheem have? Find the known.
Finding the Unknown Class 7 Short Question Answer
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Finding the Unknown Class 7 Long Short Question Answer
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Finding the Unknown Class 7 Case Based Questions
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Finding the Unknown Extra Questions for Practice
Question 1.
If 5 x-\(\frac{3}{4}=2 x-\frac{2}{3}\), then x= ?
(a) \(\frac{1}{12}\)
(b) \(\frac{1}{12}\)
(c) 36
(d) \(\frac{1}{36}\)
Question 2.
If (2 n+5)=3(3n-10) then n=? :
(a) 5
(b) 3
(c) \(\frac{2}{5}\)
(d) \(\frac{2}{3}\)
Question 3.
If \(\frac{x-1}{x+1}=\frac{7}{9}\), then x= ?
(a) 6
(b) 7
(c) 8
(d) 10
Question 4.
Solve : \(\frac{5 x}{3}\)+1=6
(a) 4
(b) 5
(c) 3
(d) 2
Question 5.
Thrice a number when increased by 6 gives 24. The number is :
(a) 6
(b) 7
(c) 8
(d) 11
Question 6.
\(\frac{2}{3}\) of a number is less than the original number by 10. The original number is :
(a) 30
(b) 36
(c) 45
(d) 60
Question 7.
If \(\frac{x}{2}-1=\frac{x}{3}+4\), then x= ?
(a) 8
(b) 16
(c) 24
(d) 30
Question 8.
If \(\frac{x-2}{3}=\frac{2 x-1}{3}-1\), then x= ?
(a) 2
(b) 4
(c) 6
(d) 8
Short Answer Type Questions :
Question 1.
Find the value of x when \(\frac{4}{5}\) x+5=13
Question 2.
Solve the equation : 3x-5=0.
Question 3.
Solve : 3+2x=1-x.
Question 4.
Solve : \(\frac{x}{2}+\frac{3}{5}=\frac{2 x}{5}\)
Question 5.
Solve the equation : \(\frac{2x}{3x}\)=18.
Question 6.
Solve : 0.5x+2.1=5.6.
Question 7.
Solve : 5x+2=3x+12.
Question 8.
Solve : 1-3x=2x+11.
Question 9.
Find the number which when multiplied by 7 is increased by 78.
Question 10.
Find three consecutive natural numbers such that the sum of the first and second is 15 more than the third.
Long Answer Type Questions :
Question 1.
Solve : \(\frac{x}{2}-1=\frac{x}{3}+4\).
Question 2.
If a number is tripled and the result is increased by 5, we get 50. Find the number.
Question 3.
If 5 is subtracted from three times a number, the result is 16. Find the number.
Question 4.
The sum of Ritu’s age and Ashu’s age is 25. Ritu is 12 years old. Write an equation to find Ashu’s age.
Question 5.
7 times a number decreased by 3 equal 18. Find the number.
Question 6.
A number is \(\frac{2}{3}\) times another number. If their sum is 70, find the numbers.
Question 7.
The ages of Sonal and Monoj are in the ratio 7: 5. Ten years hence, the ratio of their ages will be 9: 7. Find their present ages.
Question 8.
A number when added to its half gives 72. Find the number.
Question 9.
A number added to its two-thirds is equal to 55.
Question 10.
A dealer earned a profit of 5% by selling a radio for Rs. 714 . Find the cost price of radio.
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