TWO NUMBERS ARE IN THE RATIO 2:3. IF 4 BE SUBTRACTED FROM EACH THEY ARE IN THE 3:5. WHAT ARE THE NUMBERS
Answers
Step-by-step explanation:
Let the two no.s be x and y
the numbers are in the ratio 3:4 i.e; x/y = 3/4 ___ equation 1
when 4 is subtracted from each of the numbers the ratio becomes 5:7
i.e; (x-4)/ (y-4) = 5/7___ equation 2
take equation 1 and cross multiply you'll get 4x=3y and on further simplification we get x= (3/4) y
now take the second equation and do the same thing and after simplification we get 7x-28 = 5y-20 ____ equation 3
substitute the value of x i.e; (3/4)y in equation 3
7(3/4)y-28 = 5y-20
(21y/4)-28 = 5y-20
(21y/4)-5y = 28-20
(21y-20y)/4 = 8 (take 4 as L.C.M)
y/4 = 8
y= 32
now substitute y=32 in the equation x=(3/4)y
we get x as 24.
therefore 24/32= (8*3)/(8*4)= 3/4
subtracting 4 from each we get 20/28= (4*5)/(4*7)= 5/7.
which satisfies the above conditions so the two numbers x and y are 24 and 32.
Thanks and Regards
Veeraraju Pallapothu.
Let the two numbers be x and y.
x:y::3:4 or 4x = 3y or 4x - 3y = 0… (1)
(x-4):(y-4)::5:7 or 7(x-4) = 5(y-4) … (2)
Re-write (2) as
7x-28 = 5y-20, or
7x-5y = 28–20 = 8 … (3)
Multiply (1) by 5 and (3) by 3, to get
20x -15y = 0 … (4)
21x-15y = 24 …(5)
Subtract (4) from (5) to get
21x -20x = 24, or
x = 24
Now 4x = 3y or 3y = 4*24 or y = 32.
x:y = 24:32.
Check: (24–4)/(32–4) = 20/28 or 5:7.
Answer: x:y = 24:32 (option 4)
Breathe again with Philips Air Purifier.
The ratio of two numbers is 3:4. If 5 is subtracted from each of the numbers the ratio becomes 5:7. How do you find the number?
Two numbers are in the ratio of 5:7. If 3 is subtracted from each of them, the ratio becomes 2:3. What are the numbers?
Two numbers are in ratio 4:5. If 7 is subtracted from each of them the ratio becomes 3:4. What are the two numbers?
Let tge common ratio = x
than...
numerator= 3x
denominator= 4x
so, ratio = 3x/4x
now according to the question...
(3x-4)/(4x-4) = 5/7
Cross multiplying..
7(3x-4) =5(4x-4)
This implies
21x-28 =20x- 20
Or.
X= 8
Thus.. numerator = 3x = 3 x 8 = "24"
And, denominator = 4x = 4 x 8 = "32"
So ans is= 24:32
Difference between the 2 numbers remains unchanged after 4 is subtracted from each.
5 : 7 → difference in no. of units = 7–5 = 2
3 : 4 = 6 : 8 → difference in no. of units = 8–6 = 2
Difference in number of units is the same after 4 is subtracted from each number.
Number of units subtracted = 8–7 or 6–5 = 1
1 unit = 4
One of the 2 numbers is 6 units = 6 x 4 = 24
The other number is 8 units = 8 x 4 = 32