Question

two numbers are in ration 15:16. If 3 is added to each of them, the ratio becomes 16:17. find the numbers

Answer 1

Step-by-step explanation:

ANSWER

Let the two numbers be x and y.

As per condition 1, i.e., Two numbers are in the ratio 3 : 4.

The equation becomes,

y

x

=

4

3

∴4x−3y=0 ..........(1)

As per condition 2, If 4 is added to each, the ratio becomes 4:5.

The equation becomes,

y+4

x+4

=

5

4

∴5x−4y=−4 ...........(2)

Equation (1) can be written as x=

4

3y

Substituting x=

4

3y

in (2) we get,

y=16

Re substituting y=16 in (1) we get,

x=12

Hence Numbers are 12 and 16

Answer 2

☯︎ Aɴsᴡᴇʀ

we have,

ratio of two numbers is 15:16

let the numbers are 15x and 16x

and according to the question,

( if 3 is added to each of them , the ratio becomes 16:17)

$\bold{ : \implies\frac{15x + 3}{16x + 3} = \frac{16}{17} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ : \implies17(15x + 3) = 16(16x + 3) } \\ \\ \bold{ : \implies255x + 51 = 256x + 48 } \: \: \: \: \: \: \: \\ \\ \bold{ : \implies256x - 255x = 51 - 48} \: \: \: \: \: \: \: \\ \\ \bold{ : \implies \: \boxed{ \bold x = 3} \: \: \: \: \: } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

then, numbers are

• 15 × 3 = 45
• 16 × 3 = 48

therefore, numbers are 45 and 48