There are 900 creatures in a zoo as per list given below:
Question: There are 900 creatures in a zoo as per list given below: Represent the above data by a pie chart. Solution: Total number of creatures $=900$ Central angle of each component $=\left(\frac{\text { number of creatures in each type }}{\text { total number of creatures }} \times 360\right)^{\circ}$ Calculation of central angles...
Read More →The monthly income of family is ₹ 28800. The monthly expenditure of the family on various items is given below.
Question: The monthly income of family is ₹ 28800. The monthly expenditure of the family on various items is given below. Represent the above data by a pie chart. Solution: Monthly income of the family = ₹28,800 Central angle for each item $=\left(\frac{\text { Expenditure per month on various items }}{\text { Monthly income }} \times 360\right)^{\circ}$ Calculation of central angles Construction of pie chartSteps of construction 1. Draw a circle of any convenient radius. 2. Draw a horizontal ra...
Read More →The area of a square plot is
Question: The area of a square plot is $101 \frac{1}{400} \mathrm{~m}^{2}$. Find the length of one side of the plot. Solution: Let length of the square plot be a. Then, the area of square $=a^{2}$ According to the question, Area $=101 \frac{1}{400} \mathrm{~m}^{2}$[given] $\therefore$ $a^{2}=101 \frac{1}{400} \Rightarrow a^{2}=\frac{40401}{400}$ $\Rightarrow$ $a=\sqrt{\frac{40401}{400}} \Rightarrow a=\sqrt{\frac{201 \times 201}{20 \times 20}}$ $\therefore$ $a=\frac{201}{20}=10 \frac{1}{20} m$ [t...
Read More →Find the smallest square number divisible
Question: Find the smallest square number divisible by each one of the numbers 8, 9 and 10. Solution: The least number divisible by each of the numbers 8,9 and 10 is equal to the LCM of 8,9 and 10 . $\therefore \mathrm{LCM}$ of 8,9 and $10=2 \times 2 \times 2 \times 3 \times 3 \times 5=360$ Prime factors of $360=(2 \times 2) \times 2 \times(3 \times 3) \times 5$ Here, prime factors 2 and 5 are unpaired. Clearly, to make it a perfect square, it must be multiplied by $2 \times 5$, i.e. 10 . Theref...
Read More →Find three numbers in the ratio 2:3:5,
Question: Find three numbers in the ratio 2:3:5, the sum of whose squares is 608. Solution: Let us assume the three number be 2a, 3a, 5a Then, Given, sum of squares of three numbers is 608 i.e. (2a)2+ (3a)2+ (5a)2= 608 4a2+ 9a2+ 25a2= 608 38a2= 608 a2= 608/38 a2= 16 a = 16 a = (4 4) a = (42) a = 4 The numbers are, 2a = 2 4 = 8 3a = 3 4 = 12 5a = 5 4 = 20...
Read More →A king wanted to reward his advisor,
Question: A king wanted to reward his advisor, a wiseman of the kingdom. So, he asked the wiseman to name his own reward. The wiseman thanked the king, but said that he would ask only for some gold coins each day for a month. The coins were to be counted out in a pattern of one coin for the first day, 3 coins for the second day, 5 coins for the third day and so on for 30 days. Without making calculations, find how many coins will the advisor get in that month? Solution: Let the advisor get $x$ c...
Read More →A 5.5m long ladder is leaned against a wall.
Question: A 5.5m long ladder is leaned against a wall. The ladder reaches the wall to a height of 4.4m. Find^the distance between the wall and the foot of the ladder. Solution: Let the distance between the wall and the foot of the ladder be $x \mathrm{~m}$ In right angled $\triangle A B C$, by using Pythagoras theorem, we get $B C^{2}=A B^{2}+A C^{2}$ $\Rightarrow \quad(5.5)^{2}=x^{2}+(4.4)^{2}$ $\Rightarrow \quad x^{2}=(5.5)^{2}-(4.4)^{2}$ $\Rightarrow: \quad x^{2}=30.25-19.36$ $\Rightarrow \qu...
Read More →Solve each of the following in equations and represent the solution set on
Question: Solve each of the following in equations and represent the solution set on the number line. $5-2 x \mid \leq 3, x \in R$ Solution: Given: $|5-2 x| \leq 3, x \in R .$ $5-2 x \geq-3$ or $5-2 x \leq 3$ $5-2 x \geq-3$ Subtracting 5 from both the sides in the above equation $5-2 x-5 \geq-3-5$ $-2 x \geq-8$ Now, multiplying by -1 on both the sides in the above equation $-2 x(-1) \geq-8(-1)$ $2 x \leq 8$ Now dividing by 2 on both the sides in the above equation $\frac{2 x}{2} \leq \frac{8}{2}...
Read More →Rahul walks 12m North from his house and turns
Question: Rahul walks 12m North from his house and turns West to walk 35m to reach his friends house. While returning, he walks diagonally from his friends house to reach back to his house. What distance did he walk, while returning? Solution: Let Rahul walked $x \mathrm{~m}$, while returning home. In $\Delta A B C$, by using Pythagoras theorem, we get $A C^{2}=A B^{2}+B C^{2}$ $\Rightarrow \quad A C^{2}=(12)^{2}+(35)^{2}$ $\Rightarrow \quad A C^{2}=144+1225=1369$ $\Rightarrow \quad A C=\sqrt{13...
Read More →8649 students were sitting in a lecture room
Question: 8649 students were sitting in a lecture room in such a manner that there were as many students in the row as there were rows in the lecture room. How many students were there in each row of the lecture room? Solution: Let number of students in each row of the lecture room be $x$. Then, number of rows $=x$ $\therefore$ Total students $=x \times x=x^{2}$ According to the question, $x^{2}=8649$ $\Rightarrow \quad x=\sqrt{8649}$ $\therefore \quad x=93$ Hence, there are 93 students in each ...
Read More →A hall has a capacity of 2704 seats.
Question: A hall has a capacity of 2704 seats. If the number of rows is equal to the number of seats in each row, then find the number of seats in each row. Solution: Let the number of seats in each row be $x$. Then, number of rows $=$ Number of seats in each row $=x$ $\therefore$ Total seats $=x \times x=x^{2}$ According to the question, $x^{2}=2704$ $\Rightarrow \quad x=\sqrt{2704}=\sqrt{52 \times 52}$ $\Rightarrow \quad x=52$ Hence, there are 52 seats in each row....
Read More →Find the number of plants in each row,
Question: Find the number of plants in each row, if 1024 plants are arranged, so that number of plants in a row is the same as the number of rows. Solution: Let the number of plants in each row be $x$. Then, number of rows $=$ Number of plants in each row $=x$ $\therefore \quad$ Total plants $=x \times x=x^{2}$ According to the question, $x^{2}=1024$ $\Rightarrow \quad x=\sqrt{1024}=\sqrt{32 \times 32}$ $\therefore \quad x=32$ Hence, there are 32 plants in each row....
Read More →Difference of two perfect cubes is” 189.
Question: Difference of two perfect cubes is 189. If the cube root of the smaller of the two numbers is 3, then find the cube root of the larger number. Solution: Given different of two perfect cubes $=189$ and cube root of the smaller number $=3$ $\therefore$ Cube of smaller number $=(3)^{3}=27$ Let cube root of the larger number be $x$. Then, cube of larger number $=x^{3}$ According to the question, $x^{3}-27=189$ $\Rightarrow \quad x^{3}=189+27$ $\Rightarrow \quad x^{3}=216$ $\Rightarrow \qua...
Read More →Solve each of the following in equations and represent the solution set on
Question: Solve each of the following in equations and represent the solution set on the number line. $3 x-7 \mid4, x \in R$ Solution: Given: $|3 x-7|4, x \in R .$ $3 x-7-4$ or $3 x-74$ (Because $|x|a, a0$ then $x-a$ and $xa$ ) $3 x-7-4$ Now, adding 7 to both the sides in the above equation $3 x-7+7-4+7$ $3 x3$ Now, dividing by 3 on both the sides of above equation $\frac{3 x}{3}\frac{3}{3}$ $x1$ Now, $3 x-74$ Adding 7 on both the sides in above equation $3 x-7+74+7$ $3 x11$ Now, dividing by 3 o...
Read More →Solve each of the following in equations and represent the solution set on
Question: Solve each of the following in equations and represent the solution set on the number line. $\frac{5 x+8}{4-x}2, x \in R$ Solution: Given: $\frac{5 x+8}{4-x}2, x \in R$ Subtracting both the sides by 2 $\frac{5 x+8}{4-x}-22-2$ $\frac{5 x+8-2(4-x)}{4-x}0$ $\frac{5 x+8-8+2 x}{4-x}0$ $\frac{7 x}{4-x}0$ Now dividing both the sides by 7 $\frac{7 x}{7(4-x)}\frac{0}{7}$ $\frac{x}{4-x}0$ Signs of x: $x=0$ $x0$ $x0$ Signs of 4 x: $4-x=0 \rightarrow x=4$ (Subtracting 4 from both the sides, then d...
Read More →Can there be a temperature-time graph as follows? Justify your answer.
Question: Can there be a temperature-time graph as follows? Justify your answer. Solution: (i) Yes, temperature is directly proportional to time. (ii) Yes, temperature decreases with time. (iii) No, tempertaure can not change for a particular time. (iv) Yes, temperature is constant....
Read More →Explain the situations represented by the following distance-time graphs:
Question: Explain the situations represented by the following distance-time graphs: Solution: (a) Graph shows the uniform speed. (b) Moves with uniform speed and then comes to rest. (c) Moves with non uniform speed and then slowly comes to rest....
Read More →Find the side of a square whose area is
Question: Find the side of a square whose area is equal to the area of a rectangle with sides 6.4m and 2.5m. Solution: From the question it is given that, Length of rectangle = 6.4 m Breadth of rectangle = 2.5 m Area of rectangle = length breadth = 6.4 2.5 = 16 m2 And also its given in the question i.e. area of square is equal to the area of rectangle. Let us assume area of square be a. Area of square = Area of rectangle a a = 16 a2= 16 By taking square root on both side a = 16 a = (4 4) a = 42 ...
Read More →Sajal can ride a scooter constantly at a speed of 30 km/hr.
Question: Sajal can ride a scooter constantly at a speed of 30 km/hr. draw a distance-time graph for this situation.Use the graph drawn to find: (i) The time taken by Sajal to ride 75 km (ii) The distance covered by Sajal in $3 \frac{1}{2}$ hours Solution: We have, speed $=\frac{\text { distance }}{\text { time }}$ We have the following table for Distance-Time graph Time(hrs) 1 2 3 4 Distance(km) 30 60 90 120 (i) Given speed = 30 km/hr , distance = 75 km using formula we have $30=\frac{75}{\text...
Read More →Solve each of the following in equations and represent the solution set on
Question: Solve each of the following in equations and represent the solution set on the number line. $\frac{1}{x-1} \leq 2, x \in R$ Solution: Given: $\frac{1}{x-1} \leq 2, x \in R$ Subtracting 2 from both the sides in the above equation $\frac{1}{x-1}-2 \leq 2-2$ $\frac{1-2(x-1)}{x-1} \leq 0$ $\frac{1-2 x+2}{x-1} \leq 0$ $\frac{3-2 x}{x-1} \leq 0$ Signs of 3 2x: $3-2 x=0 \rightarrow x=\frac{3}{2}$ (Subtracting by 3 on both the sides, then multiplying by $-1$ on both the sides and then dividing...
Read More →How many square metres of carpet
Question: How many square metres of carpet will be required for a square room of side 6.5m to be carpeted. Solution: Given, side of square room = 6.5 m So, area of square room = 6.52 = 6.5 6.5 = 42.25 m2...
Read More →Three numbers are in the ratio 1:2:3 and
Question: Three numbers are in the ratio 1:2:3 and the sum of their cubes is 4500. Find the numbers. Solution: Let us assume the three number be a, 2a, 3a Then, Given, sum of cube of three numbers is 4500 i.e. a3+ (2a)3+ (3a)3= 4500 a3+ 8a3+ 27a3= 4500 36a3= 4500 a3= 4500/36 a3= 125 a =3125 a =3(5 5 5) a =3(53) a = 5 The numbers are, a = 5 2a = 2 5 = 10 3a = 3 5 = 15...
Read More →Solve each of the following in equations and represent the solution set on
Question: Solve each of the following in equations and represent the solution set on the number line. $\frac{1}{x-1} \leq 2, x \in R$ Solution: Given: $\frac{1}{x-1} \leq 2, x \in R$ Subtracting 2 from both the sides in the above equation $\frac{1}{x-1}-2 \leq 2-2$ $\frac{1-2(x-1)}{x-1} \leq 0$ $\frac{1-2 x+2}{x-1} \leq 0$ $\frac{3-2 x}{x-1} \leq 0$ Signs of 3 2x: $3-2 x=0 \rightarrow x=\frac{3}{2}$ (Subtracting by 3 on both the sides, then multiplying by $-1$ on both the sides and then dividing...
Read More →A bank gives 10% simple interest on deposits by senior citizens
Question: A bank gives 10% simple interest on deposits by senior citizens. Draw a line graph to illustrate the relation between the sum deposited and the simple interest earned. Find from the graph: (i) The annual interest obtainable for a investment of Rs 250 (ii) The investment one has to make in order to get an annual simple interest of Rs 70 Solution: Using $S I=\frac{P \times R \times T}{100}$ Where SI = simple interest $\mathrm{P}=$ principal $\mathrm{R}=$ rate of interest $\mathrm{T}=$ ti...
Read More →Find the length of each side of
Question: Find the length of each side of a cube if its volume is 512 cm3. Solution: From the question it is given that, Volume of the cube = 512 cm3 We know that, Volume of cube = side3 512 = side3 By taking cube root on both the side, 3512 = side Side =3(8 8 8) Side =3 (8)3 Side = 8 cm The length of each side of a cube is 8 cm....
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