Question

please give me answer of this guestion two numbers are such that the ratio between them is 3:5 if each is increased by 10 the ratio between the new numbers so formed is 5:7 .find the original. numbers

Answer 1

so 3x+10/5x+10=5/7
now 21x+70=25x+50
4x=20
x=5
original number is 3*5/5*5=15/25

Answer 2

Let the numbers be 3x and 5x respectively.


Given 3x+10:5x+10 :: 5x:7x

By ratio and proportion method
Product of extreme = Product of mean.
so 7x(3x+10) = 5x(5x+10)
$21 {x}^{2} + 70x = 25 {x}^{2} + 50x \\ - 50x + 70x = 25 {x}^{2} - 21 {x}^{2} \\ = > 20x = 4 {x}^{2}$
cancelling in this way
$20 = \frac{4x {}^{2} }{x} \\ = 20 = 4x$
so we have
$x = \frac{20}{4} \\ x = 5$
now x is 5
so 3x = 3×5. = 15
second number = 5x = 5× 5 =25.


First number is 15 and second is 25.

Hope it helps dear friend ☺️