Question

Two numbers are in the ratio 5:6 and if 4 is subtracted from each of
them. The resulting numbers are in the ratio 3: 4. Find the numbers.
​

Answer 1

Answer:

The numbers are X=10 and Y=12.

Step-by-step explanation:

Let assume two number be X and Y respectively.

               according to first condition

the ratio of number =5/6

X/Y=5/6

apply cross multiply

6X=5Y

6X-5Y=0 equation one

              according to second condition

when 4 is subtract from each number ratio becomes=3/4

X-4/Y-4=3/4

apply cross multiply

4X-16=3Y-12

4X-3Y=16-12

4X-3Y=4 equation two

subtract equation 1 by equation 2

6X-5Y=0_equation 1

-4X + 3Y=-4_equation 2

apply elemination method multiply by 4 in equatio 1 and 6 in equation 2

hence

24X-20Y=0

-24X+18Y=-24

cancle X term because oboth coffecint are same but in opposite sign

-2Y=-24

2Y=24

Y=12

y=12 put in equation one

6X-5Y=0

6X=5*12

6X=60

X=10

Answer 2

$\bf{\huge{\underline{\boxed{\sf{\red{Answer:}}}}}}$

$\bf{\underline{\underline{\rm{\green{Given:}}}}}$

• Two numbers are in the ratio 5:6
• If 4 is subtracted from each of them the resulting numbers are in the ratio 3:4

$\bf{\underline{\underline{\rm{\green{To\:find:}}}}}$

• The numbers

$\bf{\underline{\underline{\rm{\green{Solution:}}}}}$

Let x be the common multiple of the ratio 5:6

•°• Smaller number = 5x

Greater number = 6x

$\bf{\underline{\underline{\rm{\green{As\:per\:the\:question:}}}}}$

• If 4 is subtracted from each of them the resulting numbers are in the ratio 3:4

After subtracting 4,

Smaller number = 5x - 4

Greater number = 6x - 4

=> $\large\rm\frac{5x-4}{6x-4}$ = $\large\rm\frac{3}{4}$

Cross multiplying,

=> 4 ( 5x - 4) = 3 ( 6x - 4)

=> 20x - 16 = 18x - 12

=> 20x - 18x = - 12 + 16

=> 2x = 4

=> x = $\large\rm\frac{4}{2}$

=> x = 2

Substitute x = 2 in value of the ratios.

$\bf{\large{\underline{\boxed{\sf{\pink{Smaller\:number\:=\:x\:=\:5x\:=\:5\:\times\:2\:=\:10}}}}}}$

$\bf{\large{\underline{\boxed{\sf{\pink{Greater\:number\:=\:y\:=\:6x\:=\:6\:\times\:2\:=\:12}}}}}}$