TCS Digital Equations Quiz- 1

43 time the no. And 34 time the reverse no.
43(10x+ y)=34(10y+ x)
430x+ 43y= 340y+34x
430x+43y-340y-34x=0
To solve this equation become
4x-3y=0 equation=2

Sum of no. And reverse no. Is 14
X+ Y= 14 equation=1
To solve both equation value of x and y
X= 6 and y= 8
number will be 68

Ans= 25

Let the two digit number be 10x+y
Adding 2 after doubling the number is reverse of the number.
So 2(10x+y)+2 = 10y+x
19x -8y +2=0
Above equation satisfies for the value, x=2, y=5
So the number is 10*2+5= 25



Video solution:

Let x ques were correct. Therefore, (26- x) were wrong
8x−5(26−x)=08x−5(26−x)=0
Solving we get x=10



Video solution:

The primes p such that 3 < p < 100 and of the form 4x+1 are 5, 13, 17, 29, 37, 41, 53, 61, 73, 89 and 97. These are eleven in number.

The primes of the form 5y-1 are 19, 29, 59, 79, and 89 and these are five in number. Only two of these viz. 29 and 89 are in both the lists.

Both the lists taken together do not exhaust all the primes in this range, and 7, 11, 23, 31, 43, 47, 67, 71, and 83 do not appear in either of the lists.

Hence, there are only two numbers i.e., 29, and 89

Lets assume younger age = x Years.
So, elder age will be (as per question) = (x+25) years.
Given:
(X+25)-9 = 6(X-9)
By Solving the above equation
=> x=14 which is the age of younger
elder = 25+14 = 39 years.

sum of their current ages = 39+14 = 53



Video solution:

Let three consecutive odd integeres be
x,x+2,x+4
4x=6+2(x+4)
x=7
x+4=11

2^{x + y} = 2^{x - y}
2^{x + y}  =  2^{x - y} = √8 = 2^3/2
⇔   x + y = 3/2,  x - y = 3/2.
Solving these equation we get:
x = 3/2 & y = 0.

As per the given data,

We know that (x + y)² = x² + y² + 2xy

(10)² = 68 + 2xy

100 - 68 = 2xy

32 = 2xy

xy = 16

From given data

a + b = 17 and a – b = 9

By adding both the equations, we get

⇒ 2a = 26

⇒ a = 13

Substitute a = 13 in a + b = 17

⇒ 13 + b = 17

⇒ b = 4

Then value of (4a² + 4b²) = (4 × (13)² + 4 × (4)²) = 740