Question

Two numbers are such that the ratio between them is 3:5. If each is increased by 10, the ratio between the two numbers so formed is 5:7. Find the original number.

Answer 1

Answer:

15 and 25

Step-by-step explanation:

Let x , y are two numbers

x : y = 3 : 5

5x = 3y

x = 3y / 5 -----( 1 )

according to the problem given ,

if each is increased by 10 , the ratio between

the new numbers so formed is 5 : 7

( x + 10 ) : ( y + 10 ) = 5 : 7

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

7x + 70 = 5y + 50

7x + 70 - 50 = 5y

7x + 20 = 5y----( 2 )

substitute x value from equation ( 1 ) in ( 2 )

7× 3y/5 + 20 = 5y

( 21y + 100 ) / 5 = 5y

21y + 100 = 25y

100 = 25y - 21y

100 = 4y

100 / 4 = y

25 = y

Therefore ,

y = 25

put y = 25 in equation ( 1 ), we get

x = 3 × 25 / 5

x = 3 × 5

x = 15

Original numbers are x and y

= 15 and 25

I hope this helps you.

Answer 2

Answer:The two numbers are 15 and 25Step-by-step explanation:Let x and y be the required numbers. Then according to the question:$- > \frac{x}{y} = \frac{3}{5} \\ \\5x = 3y \\ \\ x = \frac{3y}{5} ...............(1) \\ \\ - > \frac{x + 10}{y + 10} = \frac{5}{7} \\ \\ 7x + 70 = 5y + 50 \\ \\ 7( \frac{3y}{5} ) + 70 = 5y + 50 \\ \\ \frac{21y}{5} + 70 = 5y + 50 \\ \\ 21y + 350 = 25y + 250 \\ \\ 25y - 21y = 350 - 250 \\ \\ 4y = 100 \\ \\ y = \frac{100}{4}=25 \\ \\ x = \frac{3y}{5} = \frac{3 \times 100}{5 \times 4} \\ \\ x= 15$Therefore the required number is given by 15 and 25.Let's verify it :$\frac{x}{y} = \frac{15}{25} = = \frac{3}{5}$

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