Question

9. If 2 is added to each of two given numbers, their ratio becomes 1:2.
However, if 4 is subtracted from each of the given numbers, the ratio
becomes 5:11. Find the numbers.​

Answer 1

Answer:

let first number is x

and second number is y

according to the question

first equation :

x+2/y+2=1/2

by cross multiply it becomes

2(x+2)=y+2

2x+4=y+2

2x-y+2=0

second equation:

x-4/y-4=5/11

by cross multiply it becomes

11(x-4)=5(y-4)

11x-44=5y-20

11x-5y-24=0

now multiply first equation by 11 and second equation by 2

22x-11y+22=0

22x-10y-48=0

by using eliminating method

-y+70=0

-y=-70

y=70

put y=70 in first equation

2x-70+2=0

2x-68=0

2x=68

x=68/2

x=34

that's the answer

hope so it's helpful

Answer 2

Given,

• If 2 is added to each of two given numbers then their ratio becomes 1:2.
• If 4 is subtracted from each of the given numbers then the ratio becomes 5:11.

To Find,

• The Number

Solution :

$\implies$ Suppose the First Number be a

And, Suppose the Second Number be b

$\mapsto \underline{\sf{\pink{According \ to \ the \ First \ Condition :}}}$

• If 2 is added to each of two given numbers then their ratio becomes 1:2.

$\implies \sf{\dfrac{a + 2}{b + 2} = \dfrac{1}{2}}$

$\implies \sf{2(a + 2) = b + 2}$

$\implies \sf{2a + 4 = b + 2}$

$\implies \sf{2a - b = 2 - 4}$

$\implies \sf{2a - b = -2}$

$\implies \boxed{\sf{b = 2a + 2}}$   1) Equation

$\mapsto \underline{\sf{\pink{According \ to \ the \ Second \ Condition :}}}$

• If 4 is subtracted from each of the given numbers then the ratio becomes 5:11

$\implies \sf{\dfrac{a - 4}{b - 4} = \dfrac{5}{11}}$

$\implies \sf{11(a - 4) = 5(b - 4)}$

$\implies \sf{11a - 44 = 5b - 20}$

$\implies \sf{11a - 5b = -20 + 44}$

$\implies \sf{11a - 5b = 24}$

║Now Put the Values of b From the Equation First ║

$\implies \sf{11a - 5(2a + 2) = 24}$

$\implies \sf{11a - 10a - 10 = 24}$

$\implies \sf{a = 24 + 10}$

$\implies \boxed{\sf{a = 34}}$

║Now Put the Value of a in First Equation ║

$\implies \sf{b = 2a + 2}$

$\implies \sf{b = 2(34) + 2}$

$\implies \sf{ b = 68 + 2}$

$\implies \boxed{\sf{b = 70}}$

Therefore,

$\boxed{\large{\bold{\red{The \ First \ Number = a = 34 }}}}$

$\boxed{\large{\bold{\red{The \ Second \ Number = b = 70}}}}$

$\rule{200}2$