13

10x-60

\(a=\frac{7}{2}\)and \(b=\frac{3}{4}\)

k=5

120⁰

54⁰

7 days

80

18 kg

14 yr

In this question, given formula for getting perime of triangle is P = 2a + 2b + 2c
Here, 2a, 2b and 2c are the length of sides of the triangle.
Hence, the perimeter of the triangle is given byth sum of sides of the triangle.

Let the age of Sunita's mother = 2x yr
Then, according to the question,
Sunita's age = \(\frac{2x}{2}\) = x [half of her mother's age
(i) After 4 yr, present age is added in given years.
Sunita's age = (x + 4) yr
∴ Her mother's age = (2x + 4) yr
(ii) Before 3 yr, given year is subtracted from present age.
∴  Sun ita's age = (x - 3) yr
and her mother's age = (2x - 3) yr

According to the question,
Tanks to collect rain water = 9
Rain water is collected per tank (in L) = x
Then, total rain water in tanks (in L)
= Number of tanks x Per tank collected rain water
= 9\(\times\)x = 9x
But in the one tank, already 200 L of water exist, then total amount of water is given by = 200 + [Total rain water in L]
= 200 + 9x or (9x + 200)L

Let the cost of 1 dozen be Rs x.
Then, cost of 3 dozen = Rs 3x
According to the question,
\(3x=54 \Rightarrow x=\frac{54}{3}=18\)
∴ The cost of one dozen = Rs 18
Hence, Rehman can buy 1 dozen of bananas.
(b) Humanity, Helpfulness, caring for others.

Let the two numbers be x and y, which has solution 2 in equation.
(i) For getting first equation, the number x is multiplied by 2, then the number is 2x. After
that, 3 is subtracted from it which results Into 1.
Hence, we have 2x - 3 = 1
On solving, 2x = 3 + 1 ⇒ 2x = 4 ⇒ x = 2
(ii) For getting second equation the number y is multiplied by 3, then the number IS 3y After that
it will be added to 4 and equal to 10
Hence, we have, 3y + 4=10
On solving, 3y=10-4 ⇒ 3y=6 ⇒ y=2 Hence, two equations are 2x - 3 = 1and 3y + 4 = 10

Given, length of bulletin board =r cm
and breadth of bulletin board = t cm
Then, perimeter of this board = 2 (r + t) cm
and area of this board =rt cm²
(a) Required length of aluminium strip = [2 (r+ t)+ 10) cm
(b) To repair one board number of nails required = x
For 15 boards, numbers of nails = 15x
(c) Area of one board = rt sq cm
Area of eight boards = 8 rt sq cm
Extra cloth for one board = 500 sq cm
Extra cloth for eight boards = 4000 sq cm
Required area of the cloth = (8rt + 4000) sq cm
(d) Charges for one board = Rs x
Charges for 23 board = Rs 23 x

a) Let number be x.
Twice the number = 2x Then,2x-13=3
(b) Let the number be x.
One-fifth of this number =\(\frac{x}{5}\)
Then,\(\frac{x}{5}\)=x-5
(c) Let the number be x.
Two-third of this number =\(\frac{2}{3}x\)
∴ \(\frac{2x}{3}=12\)
(d) Let the number be x.
Twice of this number = 2x
Then, 2x + 9 =13
(e) Let the number be x.
One-third of this number =\(\frac{x}{3}\)
Then, \(\frac{x}{3}\)-1=1

(a) Let the number be x.
Then, the required equation is x + 14 = 70
(b) Let the number be x.
Then, the required equation is x - 3 = 10
(c) Let the number be x.
Given, five times of x = 5x
∴ Required equation is 5x = 25
(d) Let the number be x.
One-third of x = \(\frac{x}{3}\)
Then, the equation is \(\frac{x}{3}\)=15
(e) Let the number be x.
Two times of this number = 2x
∴ The equation is 2x + 3 = 13

(a) Given, Anil's present age = x yr
Anil's age after 15 yr = (x + 15) yr
(b) 5 yr ago Anil's age = (x - 5) yr
5 times Anil's age, 5 yr ago = 5(x - 5) yr
(c) Given, Anil's age = x yr
Father's age = (2x + 15) yr
(d) 5 yr ago Anil's age = (x - 5) yr
Now, cousin's age = \([\frac{1}{3}(x-5)-3]\)yr
(e) Given, Anil's age = x yr
Anil's father age = (x + 20) yr
Anil's grandfather age = 2(x + 20) yr

(i) Let I be denoted by x.
We know that, a square has 4 corners and each corner is counted thrice.
∴  Total number of corners = 4\(\times\)3 = 12
By given condition, my self + total number of corners
⇒ x+12=34
Now, x=34-12=22 ⇒ x=22
By inspection, we have 22 + 12 =34
Thus, I am 22.
ii) Let I be denoted by x. There are 7 days in a week.
By given condition upcounting from x for 7, we get the sum = 23
i.e. x + 7 = 23
Now, x=23-7=16 ⇒  x=16
By inspection, we have 16 + 7 = 23
Thus, I am 16.
(iii) Let the special number be x.
Then, as per given condition take away 6 from x =whole cricket team i.e. x - 6 = 11
In cricket team, number of players = 11
Now, x = 11 + 6 = 17
⇒ x=17
By inspection, we have 17 - 6 = 11
Thus, the special number is 17.
(iv) Let I be denoted by x.
By given condition, take x out of 22 = x
⇒ 22 - x = x ⇒x + x = 22
⇒ 2x = 22 ⇒ x = 11
By inspection, we have 2\(\times\)11 = 22
Thus, I am 11.

10 marks

40 runs

5 cm

Given, the Meena is at step = 5

Also, Beena is 8 steps ahead.
∴ Beena is at step = 5 + 8 and Leena is 7 steps behind
∴ Leena is at step = 5 - 7
Now, total number of steps = 10 less than 4 times Meena's steps = 4\(\times\)Meena's steps - 10 = 45 -10
Hence, total number of steps using 5 can be expressed as (45 - 10).

Let Sarita's present age = y yr
(i) Sarita's age after 5 yr from now = (y + 5) yr
(ii) Sarita's age 3 yr back = (y - 3) yr
(iii) Given, Sarita's grandfather is 6 times of her age So,
Sarita's grandfather age = 6\(\times\)Sarita's present age =6\(\times\)y=6yyr
(iv) Given, grandmother is 2 yr younger than grandfather. Age of grandfather = 6y yr [from (iii)]
∴  Age of grandmother = [Grandfather's age - 2] yr =(6y-2)yr
(v) Given, Sarita's father's age is 5 yr more than 3 times Sarita's age.
Sarita's present age =y yr
3 times of Sarita's age = 3y yr
∴  Sarita's father age = 3\(\times\)Sarita's age + 5 = (3y + 5) yr