Question

1)A number is 4 times another number.
21 is added to both the numbers then first number becomes 7 by 4times the other number. What are the numbers ​

Answer 1

Let the numbers be x and y.

x=4y …(1)

(21+x)/(y+21) = 7/4 or

4(21+x) = 7(y+21) or

84 + 4x = 7y +147, or

4x-7y = 147–84=63 …(2)

Put the value of x from (1) in (2)

16y–7y = 9y = 63, or

y = 7 and x = 28.

Check: (28+21):(7+21)::49/28 or 7/4. Correct.

The numbers are 28 and 7.

Answer 2

Step-by-step explanation:

Let the numbers be x and y.

A number is 4 times another number,

x = 4y…Eq..1

if 21 is added to both the numbers then first number becomes 7/4 times the other number.

(x + 21)/(y + 21) = 7/4

Cross multiplication

4 (x + 21) = 7 (y + 21)

4x + 84 = 7y + 147

4x - 7y = 147 – 84

4x - 7y = 63…Eq..2

Now putting the value of x from Eq.1 to Eq..2

4 (4y) - 7y =63

16y – 7y = 63

9y = 63

y = 63/9

y = 7

One number is 7

To derive the other number, putting the value of y in Eq..1

x = 4y

x = 4 × 7

x = 28

The other number is 28

Thus the two numbers are 7 and 28

Answer the two numbers are 7 and 28

Now Checking the correctness of answer by substituting the values of both numbers in the Eq..2

4x - 7y = 63

4 × 28 - 7 × 7 = 63

112 - 49 = 63

63 = 63

Means answer is correct.