Question

CLASS 8
"COMPARING QUANTITIES"

QUES- Two numbers are in the ratio of 3 : 5 but when they are increased by 10, their ratio is 5 : 7, find the numbers.


PLEASE GIVE CORRECT ANSWERS WITH EXPLANATION. INCORRECT/ UNNECESSARY ANSWERS WILL BE REPORTED.
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Answer 1

Answer:

15 and 25

Step-by-step explanation:

3x+10/5x+10=5/7

21x+70=25x+50

25x-21x=70-50

4x=20

x=5

so

no. 15. and. 25

Answer 2

Solution :

Let the two number's be r & m respectively;

$\underbrace{\bf{1^{st}\:Case\::}}}}$

$\longrightarrow\sf{\dfrac{r}{m} =\dfrac{3}{5} }\\\\\longrightarrow\sf{5r=3m}\\\\\longrightarrow\sf{r=3m/5......................(1)}$

$\underbrace{\bf{2^{nd}\:Case\::}}}}$

$\longrightarrow\sf{\dfrac{r+10}{m+10} =\dfrac{5}{7} }\\\\\longrightarrow\sf{7(r+10) = 5(m+10) }\\\\\longrightarrow\sf{7r+70 = 5m+50}\\\\\longrightarrow\sf{7r-5m=50-70}\\\\\longrightarrow\sf{7r-5m=-20}\\\\\longrightarrow\sf{7\bigg(\dfrac{3m}{5} \bigg)-5m=-20\:\:[from(1)]}\\\\\longrightarrow\sf{\dfrac{21m}{5} -5m=-20}\\\\\longrightarrow\sf{21m-25m=-100}\\\\\longrightarrow\sf{-4m=-100}\\\\\longrightarrow\sf{m=\cancel{-100/-4}}\\\\\longrightarrow\bf{m=25}$

∴ Putting the value of m in equation (1),we get;

$\longrightarrow\sf{r=\dfrac{3\times 25}{5} }\\\\\longrightarrow\sf{r=\cancel{75/5}}\\\\\longrightarrow\bf{r=15}$

Thus;

The two number's will be 15 & 25 .