### Algebra-Solutions Ex-11.1

CBSE Class –VI Mathematics
NCERT Solutions
Chaper 11 Algebra (Ex. 11.1)

Question 1. Find the rule, which gives the number of matchsticks required to make the following matchsticks patterns. Use a variable to write the rule.
(a) A pattern of letter T as (b) A pattern of letter Z as (c) A pattern of letter U as (d) A pattern of letter V as (e) A pattern of letter E as (f) A pattern of letter S as (g) A pattern of letter A as  $2n$ (as two matchsticks used in each letter)
(b) Pattern of letter $3n$ (as three matchsticks used in each letter)
(c) Pattern of letter $3n$ (as three matchsticks used in each letter)
(d) Pattern of letter $2n$ (as two matchsticks used in each letter)
(e) Pattern of letter $5n$ (as five matchsticks used in each letter)
(f) Pattern of letter $5n$ (as five matchsticks used in each letter)
(g) Pattern of letter $6n$ (as six matchsticks used in each letter)
Question 2. We already know the rule for the pattern of letter 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?
Answer: The letter ‘T’ and ‘V’ that has pattern $2n,$ since 2 matchsticks are used in all these letters.
Question 3. 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)
Answer: Number of rows = $n$
Cadets in each row = 5
Therefore, total number of cadets = $5n$
Question 4. 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)
Answer: Number of boxes = $b$
Number of mangoes in each box = 50
Therefore, total number of mangoes = $50b$
Question 5. 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)
Answer:Number of students = $s$
Number of pencils to each student = 5
Therefore, total number of pencils needed are = $5s$
Question 6. A bird flies 1 kilometer 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)
Answer: Time taken by bird = $t$ minutes
Speed of bird = 1 km per minute
Therefore, Distance covered by bird = speed x time = $1×t=t$ km
Question 7. Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots with chalk powder as in figure). She has 8 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? Answer: Number of dots in each row = 8 dots
Number of rows = $r$
Therefore, total number of dots in r rows = $8r$
When there are 8 rows, then number of dots = 8 x 8 = 64 dots
When there are 10 rows, then number of dots = 8 x 10 = 80 dots
Question 8. 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.
Answer: Radha’s age = $x$ years
Therefore, Leela’s age = $\left(x-4\right)$ years
Question 9. 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?
Answer: Number of laddus gave away = $l$
Number of laddus remaining = 5
Total number of laddus she make = $\left(l+5\right)$
Question 10. 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?
Answer: 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 = $2x+10$

Question 11. (a) Look at the following matchstick pattern of squares. The squares are not separate. Two neighbouring 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.) (b) Figures below 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.  4 matchsticks 7 matchsticks 10 matchsticks 13 matchsticks
If we remove 1 from each then they makes table of 3, i.e., 3, 6, 9, 12, ……….
So the required equation = $3x+1$ , where $x$ is number of squares. 3 matchsticks 7 matchsticks 10 matchsticks 13 matchsticks
If we remove 1 from each then they makes table of 2, i.e., 2, 4, 6, 8, ……….
So the required equation = $2x+1$ , where $x$ is number of triangles.