Question

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.



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Answer 1

Answer :

71.4290%

Step-by-step explanation:

5/7*100%

71.4290%

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Answer 2

Solution :-

Let the numbers be x and y.

According to the first condition :-

$\longrightarrow \sf \dfrac{x}{y}= \dfrac{3}{5} \\\\\longrightarrow x = \dfrac{3}{5} y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(1)$

According to the second condition :-

$\longrightarrow \sf \dfrac{x+10}{y+10}= \dfrac{5}{7} \\\\\longrightarrow 7(x+10) = 5(y+10) \\\\\longrightarrow 7x+70 = 5y+50 \\\\\longrightarrow 7x-2y = -20 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..................(2)$

Substitute the value of x in eq(2) :-

$\longrightarrow \sf 7 \times \dfrac{3y}{5} -5y = -20 \\\\\longrightarrow \dfrac{21y}{5}-5y = -20\\\\\longrightarrow \dfrac{21y-25y}{5y} =-20 \\\\\longrightarrow 21y-25y = -100 \\\\\longrightarrow -4y = -100 \\\\\longrightarrow \bf y = 25$

Substitute y = 25 in eq(1) :-

$\longrightarrow \sf x = \dfrac{3}{5} \times 25\\\\\longrightarrow x = 3 \times 5 \\\\\longrightarrow \bf x = 15$

The two numbers are 15 and 25.