Question

solutions with proper steps of both guestion​

Answer 1

Step-by-step explanation:

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Answer 2

Given :

• Difference between the age of two cousin : 10 years.
• 15 years ago the elder cousin was twice as old as the younger one.

To Find :

• Present of the cousins.

Solution :

Let the present age of elder cousin be x year.

Let the present age of younger cousin be y year.

Case 1 :

$\mathtt{Elder\:cousin\:age\:-\:Younger\:cousin\:age\:=\:10}$

$\mathtt{x-y=10}$ _____(1)

Case 2 :

✪ Given about the age 15 years ago,

• Elder cousin → (x - 15) years
• Younger cousin →(y - 15) years

Equation :

$\mathtt{Elder\:cousin\:=\:2(Younger\:cousin)}$

➣ $\mathtt{(x-15)\:=\:2(y-15)}$

➣ $\mathtt{x-15\:=\:2y-30}$

➣ $\mathtt{x-2y\:=\:-30\:+\:15}$

$\mathtt{x-2y=-15}$ ____(2)

✪ Solve equation 1 and 2 simultaneously to find value of x and y.

✪ Subtract equation 2 from equation 1,

$\mathtt{x-y\:-\:(x-2y)\:=\:10\:-\:(-15)}$

➣ $\mathtt{x-y\:-x\:+2y\:=\:10+15}$

➣ $\mathtt{-y+2y\:=\:25}$

➣ $\mathtt{y=25}$

✪ Substitute y = 25 in equation 1,

➣ $\mathtt{x-y=10}$

➣ $\mathtt{x=10+y}$

➣ $\mathtt{x=10+25}$

➣ $\mathtt{x=35}$

• Present Age :

$\large{\boxed{\mathtt{\purple{Present\:age\:of\:elder\:cousin\:=\:x\:=\:35\:years}}}}$

$\large{\boxed{\mathtt{\purple{Present\:age\:of\:younger\:cousin\:=\:y\:=\:25\:years}}}}$

Solution 4 :

Given :

• Each student of the class contributed as many rupee as the number of students.
• Total contribution = ₹ 1156.

To Find :

• Strength of the class.

Solution :

Let the number of students be x.

Case 1:

✪ As per the given condition,

• Each student of the class contributed as many rupee as the number of students.

✪ Rupee contributed →₹ x.

Case 2 :

Total contribution → ₹ 1156.

✪ Product of number of students and rupee contributed will gives us the total contribution.

Equation :

➣ $\mathtt{x\:\times\:x\:=\:1156}$

➣ $\mathtt{x^2\:=\:1156}$

➣ $\mathtt{x\:=\:{\sqrt{1156}}}$

➣ $\mathtt{x\:=\:34}$

$\large{\boxed{\rm{\pink{Strength\:of\:the\:class\:=\:34\:students}}}}$