Question

Two numbers are in the ratio3:5.If each number is increased by 10,the ratio becomes 5:7.Then the smaller number is which?

Answer 1

Answer:

step by step explanation:

let the two numbers be 3x and 5x respectively

according to question,

if 10 is added to each number the ratio becomes 5:7

i.e......3x+10/5x+10=5/7

7(3x+10)=5(5x+10)

21x+70=25x+50

25x-21x=70-50

4x=20

x=20/4

x=5
3x=3×5=15
5x=5×5=25
so 15 is smallest

hope it helps :)

thanks!!

Answer 2

Assumption:

Let x be the unknown number.

Therefore, one number will be = 3x

Another number will be = 5x

According to our question, the condition (or) equation will be:

$\Large{\frac{(3x + 10)}{(5x + 10)} = \frac{5}{7}}$

As they are given in ratio, we can write them in fraction.

7(3x + 10) = 5(5x + 10)(cross - multiplication)

(21x + 70) = (25x + 50)

21x + 70 = 25x + 50

21x - 25x = 50 - 70

-4x = - 20

x = $\large{\frac{-20}{-4}}$

x = $\large{\frac{\cancel{-20}}{\cancel{-4}}}$

$\boxed{\bold{\mathsf{x = 5}}}$

Now, we've gotta the value of x. Now, we'll substitute this value in our assumed numbers.

One number = 3x = 3(5) = 15

Another number = 5x = 5(5) = 25

Therefore, the two numbers are 15 and 25.

Now, we'll compare this two numbers so that, we'll gotta the smallest number.

Comparing 15 and 25.

25 > 15

Therefore, the smallest number is 15.