Question

Two number are such that the ratio between them is 2:3.if each is increased by 8 the ratio between the new number so formed is 7:5.find the orignal number

Answer 1

Answer:

Step-by-step explanation:

Let the number be x

Hence the equation formed will be,

2x+8/3x+8=7/5

Now that we have formed the equation and there is nothing to simplify we shall now cross multiply.

Hence, (3x+8 )will be multiplied with 4 and (2x+8) with 5

After multiplying the equations ,the new equation will look  somewhat like this,

21x + 56 = 10 x + 40

Now to find x we must interchange their positions as when +56 will go to the other side of = it will change to -56 and vice versa.

after bringing the numbers with x together and the non variable number beside each other, the equation shall be,

21x-10x=40-56

which is nothing but 11x=(-16)

here we can see that 11 is being multiplied with x so when it goes on the other side of = it goes in the denominator of (-16)

hence now the equation will be  x= -16/11

now that we have found x we will find the other two numbers which were in the ratio 2:3

we previously wrote them as  2x:3x

hence 2x= 2 multiplied with-16/11= -32/11

and the other number which was 3x will be

3x= 3 multiplied by -16/11 = - 48/11

Hence the two numbers are -32/11 and -48/11