Question

Ubers.
Ratio between two numbers are 4 : 7. If each is increased by 20 then the ratio becomes 7:9,
find the number​

Answer 1

Answer:

A : B

4x : 7x

Now 4 is added to each number

4x+47x+4=35

=> 20x + 20 = 21x + 12

=> x = 8

∴ Smallest number is 4×8=32

Larger number is 7×8=56

Answer 2

Solution

Given :-

• Ratio of two Number = 4:7
• If they increase by 20 then, new ratio be = 7:9

Find :-

• Both Required Number.

Explanation

Let,

• First Number be = x
• Second Number be = y

Then, According to question.

Case 1.

==> x:y = 4:7

==> x/y = 4/7

==> 7x - 4y = 0______________(1)

Case 2.

==> (x+20):(y+20) = 7:9

==> (x+20)/(y+20) = 7/9

==> 9×(x+20) = 7×(y+20)

==> 9x - 7y = 140 - 180

==> 9x - 7y = -40______________(2)

Multiply by 7 in equ(1) 4 in equ(2)

We get new Equation

==> 49x - 28y = 0________________(3)

And,

==> 36x - 28y = - 160_____________(4)

Sub. equ(3) & equ(4)

==> 49x - 36x = 160

==> 13x = 160

==> x = 160/13

keep value of x in equ(3)

==> 49×160/13 - 28y = 0

==> 28y = 7840/13

==> y = (7840)/(13×28)

==> y = 1960/(13×7)

==> y = 280/13 .

Hence

• First Number be = 160/13
• Second Number be = 280/13

_________________________

Answer Verification

According to question,

==> ==> x:y = 4:7

Keep value of x & y.

==> (160/13) : (280/13) = 4:7

==> 160/13 × 13/280 = 4:7

==> 160/280 = 4/7

==> 16/28 = 4/7

Divided by 4 in L.H.S.

==> 4/7 = 4/7

L.H.S. = R.H.S.

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