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Q.1=A two digit number is four more than 6 times the sum of its digits.If 18 is subtracted from the number,the digits are reversed .Find the number.

Q2=A two digit number is such that the product of its digits is 20.If 9 is added to the number,the digits interchange their places.Find the number.

Q.3=A two digit number is 4 times the sum of its digits and twice the product of the digits.Find the number.

Q.4=Seven times a two-digit number is equal to four times the number obtained  by reversing the digits.If the difference b/w the digits is 3.Find the number.

hey vaibhav,u didn't reply to my ans. 

Ans.2.let x= once digit and y is tenth digit.
Then , number is 10y+x
So, if the digits interchange their places, then the number is 10x+y
now,
xy=20 ....(i)

10y+x+9=10x+y
or 9x-9y=9
or x-y=1 ..(ii)
From (i) and (ii) , we get
x(x-1)=20=4X5
x=4 or 5 , but as x-y=1 , then x=5 and y=4
The number is 45.

Ans :- 2

let the digit at one's place = y and the digit at ten's place = x .......

So, number of 10x + y .... if the digits r reversed .... then the number = 10y + x .....

According to question :-

x * y = 20 ---> x = 20 / y ......(I) ...

Acoording to question :-

10x + y + 9 = 10y + x

----> (10 * 20)/y + y + 9 = 10y + 20 / y ..  [substituting values of x from I] ...

----> 200 / y + y + 9 = 10y + 20 / y

----> (200 + y² + 9y) / y = (10y² + 20) / y

----> y² + 9y + 200 = 10y² + 20

----> 9y² - 9y - 180 = 0

----> y² - y - 20 = 0

----> y² - 5y + 4y - 20 = 0

----> y(y -  5) + 4(y - 5) = 0

----> y = 5 or -4

----> y = 5   [rejecting the -ve value] ....

and x = 20 / y = 20 / 5 = 4 ....

So, number = 10x + y = 40 + 5 = 45 ... (ans) ... 

Hope this helps !!!

Ans - 4 :-

let the digit at one's place = y and the digit at ten's place = x .......

So, number of 10x + y .... if the digits r reversed .... then the number = 10y + x .....

A.T.Q :-

7(10x + y) = 4(10y + x)

----> 70x + 7y = 40y + 4x

----> 66x - 33y = 0 .........

----> 2x - y = 0 ..... (I) ..

Also ... y - x = 3 ---> x = y - 3 ....

Substyituting value of y in eqn I ...

2x - y = 0

---> 2(y - 3) - y = 0

---> 2y - 6 - y = 0

---> y = 6 .....

and x = y - 3 = 3 ..

So, number = 10x + y = 36 ....(ans) ..

Hope this helps !!

Ans :- 3

let the digit at one's place = y and the digit at ten's place = x .......

So, number of 10x + y .... 

A.T.Q :-

4(x + y) = 10x + y

----> 4x + 4y = 10x + y

----> 3y = 6x

----> y = 2x ...... (I) ....

2xy = 10x + y

----> 2 * x * 2x = 10x + 2x  [substituting value of y friom (I)] ...

----> 4x² = 12x

----> x² = 3x

----> x² - 3x = 0

----> x(x - 3) = 0

----> x = 0 or 3

----> x = 3 .....

So, y = 2x = 6 ...

So, number = 10x + y = 36 ... (ans) ...

Hope this helps !!!

and friend ...... there's no need to write dat u r a paid member ............ it's unnecessary ....

 Ans1--->

Let the unit digit be x and tens digit be y.

Therefore Two digit number= 10y+x

As per question,

6(x+y)+4= 10y+x

=> 6x+6y+4=10y+x

=>4y-5x=4-----(1)

According to next given condition,

10y+x-18=10x+y

=> 9y-9x-18=0

=> y-x=2-----(2)

=> y=(x+2)----(3)

Putting the value of y in (1), we get,

4(x+2)-5x=4

=> 4x+8-5x=4

=> -x= -4

=> x=4

Now,

y=x+2=4+2=6

Therefore value of x is 4 and y is 6

Required Answer-----> Number is 10y+x= 10*6+4= 64

 Ans 2---->

Let the unit digit be x and tens digit be 'y'

Then two digit nuber= 10x+y

If digits are reversed = 10y+x

According to question,

xy=20 -----(1)

Another Condition,

10x+y+9= 10y+x

=> 9x-9y+9=0

=> x-y+1=0

=> x-y= -1 -----(2)

=> x= (y-1) -----(3)

Putting the value of x in equation 1,

(y-1)(y)=20

=> y2-y-20=0

=> y-5y+4y-20=0

=> y(y-5)+4(y-5)=0

=> y+4=0 or y-5=0

=> y= -4 or y=5

Since y can't be negative,

y=5

Now,

xy=20 => x=20/y

=> x=20/5=> x=4

Value of x is 4 and y is 5

Required Answer---> Number= 10x+y= 10*4+5=45

*Let unit digit be 'y' and tens digit be 'x'

 Ans3----> 

Let units digit be 'x' and tens digit be 'y'

Therefore two-digit number= 10y+x

According to given condition in question,

4(x+y)=10y+x

=> 4x+4y=10y+x

=> 3x-6y=0

=> x=2y -----(1)

According to second condition,

2xy=10y+x

From equation (1),

2(2y)y=10y +2y

=> 4y²=12y

=> y²=3y

=> y²-3y=0

=> y(y-3)=0

=> y=0 or y-3=0 => y=0 or y=3

Since y can't be zero,

y=3

x=2y

=> x=2(3)=6

Therefore value of x is 6 and y is 3

Required Answer---> Number is 10y+x= 10*3+ 6= 30+6 =36

 Answer4----> Let units digit be x and tens digit be y

Two digit number= 10y+x

If number is reversed, then number= 10x+y

According to given condition,

7(10y+x)= 4(10x+y)

=> 70y+7x =40x+4y

=> 70y-4y= 40x-7x

=> 66y =33x

=> 2y=x ------(1)

Next condition,

x-y=3 ----(2)

=> x=3+y ----(3)

Substituting the value of (3) in(1)

2y= 3+y

=> y=3

x=2y

=> x= 2*3=6

Required Answer---> The number is 10y+x= 10*3+6= 30+6= 36

Hope it helps!!!

Cheers!!!

Keep smiling!!!

Satyajit--- gr8 answers!!! thumps up!!