NCERT Solutions for Class 6 Maths - Algebra

Exercise 11.1

Q1. Find the rule which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.
(a) A pattern of letter T as  
Ans:  Pattern of letter
So,
For 1T, Number for Matchsticks = 2
For 2T, Number for Matchsticks = 4
For 3T, Number for Matchsticks = 6
So, we write
Number of matchsticks = 2n
where, n = Number of T

(b) A pattern of letter Z as
Ans: Pattern of letter  
So,
For 1Z, Number of matchsticks = 3
For 2Z, Number of matchsticks = 6
For 3Z, Number of matchsticks = 9
So, we write,
Number of matchsticks = 3n
where n = Number of Z

(c) A pattern of letter U as
Ans: Pattern of letter  
So,
For 1U, Number of matchsticks = 3
Similarly
For 2U, Number of matchsticks = 6
For 3U, Number of matchsticks = 9
So, we write,
Number of matchsticks = 3n
where n = Number of U

(d) A pattern of letter V as
Ans: Pattern of letter
So,
For 1V, Number of matchsticks = 2
Similarly
For 2V, Number of matchsticks = 4
For 4V, Number of matchsticks = 6
So, we write,
Number of matchsticks = 2n
where n = Number of V 

(e) A pattern of letter E as
Ans: Pattern of letter
So,
For one E, Number of matchsticks = 5
For 2E, Number of matchsticks = 10
For 3E, Number of matchsticks = 15
So, we write,
Number of matchsticks = 5n
where, n = Number of E

(f) A pattern of letter S as
Ans: Pattern of letter  
So,
For one S, Number of matchsticks = 5
For 2S, Number of matchsticks = 10
For 3S, Number of matchsticks = 15
So, we write,
Number of matchsticks = 5n
where, n = Number of S

(g) A pattern of letter A as
Ans: Pattern of letter  
So,
For 1A, Number of matchsticks = 6
For 2A, Number of matchsticks = 12
For 3A, Number of matchsticks = 18
So, we write
Number of matchsticks = 6n
where n = Number of A

Q2. We already know the rule for the pattern of letters L, C and F. Some of the letters from Q.1 (given above) give us the same rule as that given by L. Which are these? Why does this happen?
Ans: We know that T requires only two matchsticks. So, the pattern for letter T is 2n. Among all the letters given in question 1, only T and V are the letters which require two matchsticks. Hence, (a) and (d).

Q3. Cadets are marching in a parade. There are 5 cadets in a row. What is the rule which gives the number of cadets, given the number of rows? (Use n for the number of rows.)
Ans: Number of rows = n
Cadets in each row = 5
Total number of cadets = number of cadets in each row × number of rows = 5n

Q4. If there are 50 mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes? (Use b for the number of boxes.)
Ans: Number of boxes = b
Number of mangoes in each box = 50
Therefore, total number of mangoes = number of mangoes in a box × number of boxes = 50b

Q5. The teacher distributes 5 pencils per student. Can you tell how many pencils are needed, given the number of students? (Use s for the number of students.)
Ans: Number of students = s
Number of pencils to each student = 5
The total number of pencils needed are = number of pencils to each student × number of students = 5s

Q6. A bird flies 1 kilometre in one minute. Can you express the distance covered by the bird in terms of its flying time in minutes? (Use t for flying time in minutes.)
Ans: Time taken by bird = t minutes
Speed of bird = 1 km per minute
Therefore, Distance covered by bird = speed x time = 1 x t = t km

Q7. Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots) with chalk powder. She has 9 dots in a row. How many dots will her Rangoli have for r rows? How many dots are there if there are 8 rows? If there are 10 rows?

Ans: Number of dots in a row = 9
Number of rows = r
Total number of dots in r rows = Number of dots in a row × number of rows = 9r
Number of dots in 8 rows = 8 × 9= 72
Number of dots in 10 rows = 10 × 9= 90

Q8. Leela is Radha’s younger sister. Leela is 4 years younger than Radha. Can you write Leela’s age in terms of Radha’s age? Take Radha’s age to be x years.
Ans: Given that,
Leela is 4 years younger than Radha
So,
Leela's Age = Radha's age - 4
Let Radha's age = x years
So, Leela's age = x - 4 years
where x = Radha's age

Q9. Mother has made laddus. She gives some laddus to guests and family members; still, 5 laddus remain. If the number of laddus mother gave away is l, how many laddus did she make?
Ans: Number of laddus gave away = l
Number of laddus remaining = 5
Total number of laddus = (l + 5)

Q10. Oranges are to be transferred from larger boxes into smaller boxes. When a large box is emptied, the oranges from it fill two smaller boxes and still, 10 oranges remain outside. If the number of oranges in a small box are taken to be x, what is the number of oranges in the larger box?
Ans: Number of oranges in one box = x
Number of boxes = 2
Therefore, total number of oranges in boxes = 2x
Remaining oranges = 10

Thus, number of oranges = 2x + 10

Q11: (a) Look at the following matchstick pattern of squares (Fig 11.6). The squares are not separate. Two neighboring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks

in terms of the number of squares. (Hint: If you remove the vertical stick at the end, you will get a pattern of Cs)
Ans: We may observe that in the given matchstick pattern, the number of matchsticks are 4, 7, 10 and 13, which is 1 more than thrice the number of squares in the pattern

Therefore the pattern is 3x + 1, where x is the number of squares

(b) Fig 11.7 gives a matchstick pattern of triangles. As in Exercise 11 (a) above, find the general rule that gives the number of matchsticks in terms of the number of triangles.

Ans: We may observe that in the given matchstick pattern, the number of matchsticks is 3, 5, 7 and 9 which is 1 more than twice the number of triangles in the pattern.
Therefore the pattern is 2x + 1, where x is the number of triangles.