Edudel, Directorate of Education Govt. of NCT of Delhi Class 6 Mental Maths Chapter 11 Algebra Questions Solution. In this chapter, there is total 50 math problems. We have given each questions solution step by step.
1.) Express the perimeter of square of the side x units.
Answer:
Perimeter of square = 4 × sides
Side = x units
Perimeter of square = 4 × x
Perimeter of square = 4x units
2.) Express the perimeter of rectangle of length 5 cm and breadth y cm.
Answer:
Perimeter of rectangle = 2 × ( Length + Breadth)
Length of rectangle = 5 cm
Breadth of rectangle = y cm
Perimeter of rectangle = 2 × ( 5 + y)
Perimeter of rectangle = (10 + 2y) cm
3.) In a N.C.C. parade, there are 12 cadets in a row. What is the rule which gives the total number of cadets, if the number of rows is z?
Answer:
1 Row = 12 cadets
No. of rows = z
Total no. of cadets = 12 × no. of rows
Total no. of cadets = 12z
4.) What is the rule for finding the next number in the following series:
I.) 2, 4, 6, 8, 10 ………
II.) 3, 7, 11, 15 ……….
III.) 5, 10, 15, 20 ……….
Answer:
I : The rule for finding the next number = 2n
We get next number in the series as 2, 4, 6, 8, 10, 12
2×1 = 2
2×2 =4
2×3 = 6
2×4 = 8
2×5 = 10
2×6 = 12
II : The rule for finding the next number = 4n -1
We get next number in the series as 3, 7, 11, 15, 19
(4×1) -1 = 3
(4×2)-1 = 7
(4×3) -1 = 11
(4×4) -1 = 15
(4×5) -1 = 19
III : The rule for finding the next number = 5n
We get next number in the series as ) 5, 10, 15, 20, 25
5×1 =5
5×2 = 10
5×3 = 15
5×4 = 20
5×5 = 25
5.) In a Rangoli, there are 6 dots in every row. What is the total number of dots if there are ‘z’ rows?
Answer:
1 row = 6 dots
z row = 6 × z
No. of dots in z rows = 6z
6.) Express the perimeter of regular octagon of side ‘p’ units.
Answer:
Regular octagon of side = ‘p’ units.
Perimeter of regular pentagon = 5 × length of side
Perimeter of regular pentagon = 5 × p
Perimeter of regular pentagon = 5p
7.) 6 chocolates were left with Manoj after he gave ‘t’ chocolates to his friend Raj. How many total chocolates Manoj had?
Answer:
Chocolates Manoj gave to Raj = t
Chocolates left with Manoj = 6
Total chocolates Manoj had = Chocolates Manoj gave to Raj + Chocolates left with Manoj
Total chocolates Manoj had = 6 + t
8.) Express the perimeter of isosceles triangle whose equal sides are of 5 cm and third side of ‘y’ cm.
Answer:
Equal sides = 5 cm
Third side or unequal side = ‘y’ cm
Perimeter of isosceles triangle = 2(equal sides) + unequal side
Perimeter of isosceles triangle = 2 (5) + y
Perimeter of isosceles triangle = 10 + y
9.) Sheena got “x” marks in English and 50 marks in Hindi. What are the total marks in two subjects?
Answer:
Marks scored in English = x marks
Marks scored in Hindi = 50 marks
Total marks scored in 2 subjects = 50 + x
10.) Ashu writes one page in ‘y’ hours. How many pages can he write in 10 hours?
Answer: ashu writes ,
No. of pages write in y hours = 1 page
No. of pages write in 10 hours = 10 × y
No. of pages write in 10 hours = 10y
11.) 12 subtracted from a.
Answer: a – 12
12.) 10 added to b.
Answer: b + 10
13.) P multiplied by 5.
Answer: 5p
14.) C divided by 9.
Answer: c/9
15.) ‘a’ multiplied by (– 7).
Answer: – 7a
16.) 5 times m added to 8.
Answer: 8 +5m or 5m + 8
17.) 10 times x added to (– 15).
Answer: -15 + 10x or 10x -15
18.) 24 subtracted from 4 times q.
Answer: 4q – 24
19.) 12 less than 4y.
Answer: 4y -12
20.) Cost of (x + 5) kg of rice, if cost of 1kg rice is Rs 20.
Answer: 1 Kg of rice = 20
Cost of (x +5) kg rice = (x +5) × 20
Cost of (x +5) kg rice = Rs (20x + 100)
21.) a + 5
Answer: 5 added to a
22.) y – 8
Answer: 8 subtracted from y
23.) 8 – z
Answer: z subtracted from 8
24.) 4x + 5
Answer: 5 is added to 4 times of x
25.) (5y+5)/ 2
Answer: Half of sum 5 times y and 5
26.) x + 9 = 15
Answer:
x = 15 -9
x = 6
27.) m – 2 = 10
Answer:
m = 10 +2
m = 12
28.) m/4 = 6
Answer:
m = 6 × 4
m =24
29.) 2a + 3 = 13
Answer:
2a = 13 – 3
2a =10
a = 10/2
a = 5
30.) 8m = 64
Answer:
m = 64/8
m = 8
31.) 8t –5 = 3
Answer:
8t = 3 +5
8t = 8
t = 8/8
t =1
32.) – 3p + 9/2 = 0
Answer:
3p = 9/2
p = (9/2×3)
p = 9 /6
p = 3/2
33.) x/2 + 3 = 13
Answer:
x/2 = 13 – 3
x/2 = 10
x = 10/2
x = 5
34.) 4x -2 = 3 – x
Answer:
4x + x = 3 +2
5x = 5
x = 5/5
x = 1
35.) (5x -9)/3 = 7
Answer:
(5x -9) = 7 × 3
(5x -9) = 21
5x = 21 + 9
5x = 30
x = 6
36.) Sum of two integers is −83. If one of them is −93 , then what is the second integer?
Answer:
Let Second integer be a
One integer = – 93 – – – ( given )
a + (-93) = – 83 – – – ( given)
a = – 83 + 93
a = 10
Second integer is 10
37.) I am an integer. If 21 is subtracted from me I become 9. Who am I ?
Answer:
I = integer – – – – – ( given)
I – 21 = 9 – – – – – ( given)
I = 9 + 21
I = 30
38.) The sum of two integers is −25. If one of them is – 50, then find the other integer.
Answer:
Let Second integer be a
One integer = – 50 – – – ( given )
a + (-50) = – 25 – – – ( given)
a = 25
39.) If sum of two angles is 180⁰ and greater angle is 5 times the smaller angle, then what are the measures of both angles?
Answer:
Let angle 1 = a
Angle 2 = b
a + b = 180⁰ – – – – – (given)eq 1
5a + a = 180⁰ – – – – – (given)
6a = 180⁰
a = 180 /6
a = 30⁰
Put value of a in eq 1, we get
30 + b = 180
b = 180 – 30
b = 150⁰
Measure of both angles are 30⁰ and 150⁰
40.) The length of rectangular park is thrice its breadth. If perimeter of park is 640 m, then what are the dimensions of park?
Answer:
Perimeter of rectangular park = 640 m
Length = 3 × breadth – – – – ( given ) eq1
Perimeter of rectangular park = 2 × ( length + breadth ) —- eq2
Putting values in eq2 , we get
640 = 2 ×(3b + b)
4b = 640/2
4b = 320
b = 320/4
b = 80 m
Breadth = 80 m
Put value of breadth in eq1 , we get
Length = 3 × 80
Length = 240 m
The dimensions of park is 240 m and 80 m
41.) Fare for hiring a taxi is Rs 20 for first km, then Rs.10 for every additional kilometre travelled. What is the taxi fare for travelling 12 kilometres?
Answer:
Fare for 1st km = Rs 20
Total distance travel = 12 km
Rs.10 for every additional kilometer travelled
= ( 10× additional km) – – – – – (given)
Fare for 12 km = Fare for 1st km + Fare for additional km
Fare for 12 km = ( 20 + (10× additional km))
Fare for 12 km = ( 20 + (10 x 12))
Fare for 12 km= Rs130
42.) Father is 5 times as old as his son. Sum of their ages is 54 years. What are their ages?
Answer:
Let the age of Father be a
The age of son = b
Father is 5 times as old as his son
a = 5b – – – – – ( given) eq1
a + b = 54 – – – – ( given )eq2
put value of a in eq 2, we get
5b + b = 54
6b = 54
b = 54/6
b = 9
Put value of 9 in eq 1
a = 5 × 9
a = 45
The age of Father is 45 years
The age of son = 9 years
43.) On adding 21 to integer x the result is−9 What is the value of x
Answer:
x + 21 =( – 9) – – – – (given)
x = – 9 – 21
x = – 30
44.) Anita got 45 marks in English, 48 marks in Hindi, x marks in Mathematics, 32 marks in Science and y marks in Social Science. Find the total marks she got.
Answer:
Marks in English = 45 marks
Marks in Hindi = 48 marks
Marks in Mathematics = x
Marks in Science = 32
Marks in Social Science = y
Total marks = Marks in English + Marks in Hindi + Marks in Mathematics + Marks in Science + Marks in Social Science
Total marks = 45 + 48 + x + 32 + y
Total marks = 125 + x + y
45.) The height of plant is 12 cm. If it increases by x cm everyday, then what will be its height after 10 days?
Answer:
Plant height = 12cm
Increase in height/ day = x cm
Increase in height after 10 days = 10x
Height after 10 days = plant height + increase in height
Height after 10 days = (12 + 10x) cm
46.) If 4 is subtracted from 5 times a number q the result is 21. What is the value of q
Answer:
5q – 4 = 21
5q = 21 + 4
5q = 25
q = 25/5
q = 5
47.) Find the value of y in 1/5 (2y +3) = 19
Answer:
Open the bracket
2y +3 = 19 × 5
2y + 3 = 95
2y = 95 – 3
y = 92/2
y = 46
48.) Two third of a number is 16, find the number.
Answer:
Let the number be a
(2/3) a = 16
a = (16 ×3)/2
a = 24
Number is 24
49.) Rahul’s age is x years. Rahul is 4 years older than Reeta. If the sum of their ages is 20 years, what will be their ages?
Answer :
Age of Rahul = x years
Let age of reeta = y
Age of Reeta = (4 + x) years – – – – (given)
y = 4 + x – – – – eq1
x + y = 20 – – – – ( given) eq2
Put value of y in eq2, we get
x + 4 + x = 20
2x = 20 – 4
x =16/2
x = 8 years
Put value of x in eq1, we get
y = 4 + 8
y = 12 years
Age of Rahul is 8 years and Age of Reetais 12 years
50.) Complete the following table: –
Answer:
Others Chapter Solution:
Chapter 7 |
Fractions |
Chapter 8 |
|
Chapter 10 |