Question

two numbers are such that the ratio between them is 3 : 5 if each is increased by 10 the ratio between the new number so formed is 5:7. find the original number

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Answer 1

Answer:

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.

:

Let x = the multiplier

then

3x = one number

5x = the other number

:

"If each is increased by 10, the ratio between the new numbers so formed is 5:7."

%28%283x%2B10%29%29%2F%28%285x%2B10%29%29 = 5%2F7

Cross multiply

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

:

25x + 50 = 21x + 70

25x - 21x = 70 - 50

4x = 20

x = 20/4

x = 5 is the multiplier

then

3(5) = 15 is the 1st number

5(5) = 25 is the 2nd number

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Answer 2

$\large{ \bold{ \red{ \underline{ \underline{Question...}}}}}$

Two numbers are such that the ratio between them is 3 : 5 if each is increased by 10 the ratio between the new number so formed is 5:7. find the original number..?

$\large{ \bold{ \green{ \underline{ \underline{Answer...}}}}}$

$\large{ \sf{the \: no.s \: are \: 15 \: and \: 25}}$

$\large{ \bold{ \red{ \underline{ \underline{Solution...}}}}}$

$\sf{ \purple{ \to \: given..}}$

• Ratio of numbers initially = 3:5
• 10 is added to each numbers
• Ratio of new no.s = 5:7

$\sf{ \purple{ \to \: to \: find...}}$

• Original Number....?

$\large{ \sf{ \to \: let \: the \: numbers \: be \: 3x \: and \: 5x}} \\ \\ \large{ \red{ \sf{ \to \: 10 \: is \: added \: to \: both}}} \\ \large{ \sf{ \red{ \to \: new \: ratio = \frac{5}{7} }}} \\ \\ \large{ \sf{ \to \: then \: \: \frac{3x + 10}{5x + 10} = \frac{5}{7} }} \\ \\ \large{ \sf{ \green{ \to \: cross \: multipy \: it...}}} \\ \\ \large{ \sf{ \to \: 7(3x + 10) = 5(5x + 10)}} \\ \\ \large{ \sf{ \to \: 21x + 70 = 25x + 50}} \\ \\ \large{ \sf{ \to \: 4x = 20}} \\ \\ \large{ \sf{ \to \: x = 5}} \\ \\ \large{ \red{ \sf{ \boxed{the \: no.s \: are \: 3 \times 5 = 15 \: and \: 5 \times 5 = 25}}}}$

$\large{ \bold{ \orange{ required \: answer \: is \: 15 \: and \: 25}}}$