To do:We have to tell whether the given events are certain to happen, impossible, can happen but not certain.Solution:(i) Event: You are older today than yesterday. We keep growing older with time.So, it is certain to happen.(ii) Event: A tossed coin will land heads up.Probability: When a coin is tossed, ... Read More

Given: Total number of marbles from 1 to 6 marked in a box $=6$.To do: We have to find:(i) The probability of drawing a marble with the number 2.(ii) The probability of drawing a marble with the number 5.Solution:Here, The total number of possible outcomes: $n(S)=6$As known, Probability $=\frac{ \text ... Read More

Given:A coin is flipped to decide which team starts the game. To do:We have to find the probability that our team will start.Solution:A coin has two possible outcomes Head {H} and Tail {T}.Hence, the total number of outcomes will be 2.So, $n(S)=2$As the Probability of getting a head or tail is ... Read More

To do:  We have to solve the given riddle.Solution:Let the required number be $x$$7\times x + 50 = 300 - 40$$7x+50= 260$$7x = 260 - 50$$7x= 210$$x = \frac{210}{7}$$x= 30$So, the required number is 30.

To do:We have to solve the given questions.Solution:(a) Number of marbles Irfan has $=37$. Let the number of marbles Parmit has be $x$.According to question, $5\times x+7=37$$5x=37-7$$5x=30$$x=\frac{30}{5}$$x=6$Therefore, Parmit has 6 marbles.(b) Let the age of Laxmi be $x$. Age of Laxmi’s father $=49$ yearsAccording to question, $3\times x+4=49$$3x=49-4$$3x=45$$x=\frac{45}{3}$$x=15$Therefore, Laxmi’s age ... Read More

To do:We have to solve the given questions.Solution:(a) Highest score $=87$. Let the lowest marks be $x$According to question, Highest marks obtained $= 2\times x+7$$87=2x+7$$87-7=2x$$80=2x$$x=\frac{80}{2}$$x=40$(b) Let one of the base angles be $b$. Since the triangle is isosceles, the other base angle will also be $b$.Vertex angle $=40^{\circ}$.The sum of ... Read More

To do:We have to set up equations and solve them to find the unknown numbers in the given cases.Solution:(a) Let the number be $x$.According to the question, $8\times x+4=60$$8x=60-4$$8x=56$$x=\frac{56}{8}$$x=7$(b) Let the number be $y$.According to question, $\frac{1}{5}(y)-4=3$$\frac{y}{5}=3+4$$\frac{y}{5}=7$$y=7\times5$$y=35$(c) Let the number be $x$.According to question, $\frac{3}{4}(x)+3=21$$\frac{3x}{4}=21-3$$\frac{3x}{4} =18$$x =18\times \frac{4}{3}$$x=6\times4$$x=24$(d) Let the ... Read More

To do:We have to(a) Construct 3 equations starting with $x=2$(b) Construct 3 equations starting with $x=-2$Solution:(a) Equations starting with $x=2$(i) $x=2$Multiplying both sides by $10$, $x \times 10=2\times10$$10x=20$Adding $2$ to both sides, $\Rightarrow 10x+2=20+2$$\Rightarrow 10x+2=22$(ii) $x=2$Multiplying both sides by 5, $x \times5=2\times5$$5x=10$Subtracting 3 from both sides, $\Rightarrow 5x-3=10-3$$\Rightarrow 5x-3=7$(iii) $x=2$Multiplying ... Read More

To do:We have to solve the given equations.Solution:(a) $4=5(p-2)$$\Rightarrow 4=5p-10$$\Rightarrow 5p=4+10$$\Rightarrow 5p=14$$\Rightarrow p=\frac{14}{5}$(b) $-4=5(p-2)$$\Rightarrow -4=5p-10$$\Rightarrow -4+10=5p$$\Rightarrow 6=5p$$\Rightarrow p=\frac{6}{5}$(c) $16=4+3(t+2)$$\Rightarrow 16=4+3t+6$$\Rightarrow 16-10=3t$$\Rightarrow 6=3t$$\Rightarrow t=\frac{6}{3}$$\Rightarrow t=2$(d) $4+5(p-1)=34$$\Rightarrow 4+5p-5=34$$\Rightarrow 5p-1=34$$\Rightarrow 5p=34+1$$\Rightarrow 5p=35$$\Rightarrow p=\frac{35}{5}$$\Rightarrow p=7$(e) $0=16+4(m-6)$$\Rightarrow 0=16+4m-24$$\Rightarrow 0=4m-8$$\Rightarrow 8=4m$$\Rightarrow m=\frac{8}{4}$$\Rightarrow m=2$Read More

To do:We have to solve the given equations.Solution:(a) $2(x+4)=12$$\Rightarrow 2x+8=12$$\Rightarrow 2x=12-8$$\Rightarrow 2x=4$$\Rightarrow x=\frac{4}{2}$$\Rightarrow x=2$(b) $3(n-5)=21$$3n-15=21$$\Rightarrow 3n=21+15$$\Rightarrow 3n=36$$\Rightarrow n=\frac{36}{3}$$\Rightarrow n=12$(c) $3(n-5)=-21$$\Rightarrow 3n-15=-21$$\Rightarrow 3n=-21+15$$\Rightarrow 3n=-6$$\Rightarrow n=\frac{-6}{3}$$\Rightarrow n=-2$(d) $-4(2+x)=8$$\Rightarrow -8-4x=8$$\Rightarrow -4x=8+8$$\Rightarrow -4x=16$$\Rightarrow x=\frac{-16}{4}$$\Rightarrow x=-4$(e) $4(2-x)=8$$\Rightarrow 8-4x=8$$\Rightarrow -4x=8-8$$\Rightarrow -4x=0$$\Rightarrow x=0$Read More