Question

There are two numbers such that if 7 is added to the smaller number then sum becomes double to the larger number. And if 4 is added to the larger number it becomes three times of the smaller one. Find the two numbers.​

Answer 1

Answer:

The two numbers are 3 and 5.

Step-by-step explanation:

Let the smaller number be x

Let the larger number be y

2y=7+x

3x=4+y

_______

2y–x=7(—x+2y=7)×1. ~1

3x–y=4(+3x–y=4)×2. ~2

----------------------

–x+2y=7

+6x-2y=8

------------- add

5x=15

x=3

Put x=3 in eqn.1

2y–3=7

2y=7+3

y=10/2

y=5

Therefore,x=3 and y=5

Therefore,the two numbers are 3 and 5

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption

$\textbf{\underline{Smaller\;number\;be\;p}}$  

Also,

$\textbf{\underline{Larger\;number\;be\;t}}$  

So,

p + 7 = 2t

p - 2t = -7 ........ (1)

Also,

t + 4 = 3p

t = 3p - 4 .......... (2)

Putting value of t in (1)

p - 2(3p - 4) = -7

p - 6p + 8 = -7

-5p = -7 - 8

-5p = -15

$\rm \: \: \: \: \: \: \: \: \:p=\dfrac{\cancel{-15}}{\cancel{-5}}$

p = 3

Putting value of p in (2)

3 × 3 - t = 4

9 - t = 4

t = 9 - 4

t = 5

Hence,

$\textbf{\underline{Smaller\;number=3}}$  

$\textbf{\underline{Larger\;number=5}}$