Question

Two numbers are in the ratio 4:5 . If 5 is added to each number , the ratio becomes 13: 16.Find the number ​

Answer 1

${\huge{\underline{\underline{\bf{\maltese \; Question :-}}}}}$

Q - Two numbers are in the ratio 4 : 5 . If 5 is added to each number , the ratio becomes 13 : 16 . Find the numbers .

${\huge{\underline{\underline{\bf{\maltese\;Answer\checkmark}}}}}$

Let the two numbers be 4x and 5x .

Now ,

According to the Question :

$\rm \: 4x + 5 \: : 5x + 5 = 13 : 16$

$\mapsto \rm \: \frac{4x + 5}{5x + 5} = \frac{13}{16}$

cross multiplying

$\mapsto \rm \: (4x + 5)16 = (5x + 5)13$

$\mapsto \rm \: 64x + 80 = 65x + 65$

$\mapsto \rm \: 65x - 64x = 80 - 65$

$\mapsto \boxed{ \rm \: x = 15}$

So ,

• First Number = 4x = 4×15 = 60 .
• Second Number = 5x = 5×15 = 75 .

Answer 2

☆Find: -

The Number

☆Solution:-

Let The Numbers Be 4x and 5x

4x + 5 : 5x +5 = 13 : 15

$\frac{4x + 5}{5x + 5} = \frac{13}{16}$

$(4x + 5) \: 16 = (5x + 5) \: 13$

$64x + 80 = 65x + 65$

$65x - 64x = 80 - 65$

$x = 15$

${ \huge {\underline {\underline {\mathtt {\pink{AnSwEr♡}}}}}}$

1st Number= 4x = 4×15 = 60

2nd Number= 5x = 5×15= 75

Hope it helps you!!

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