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The sum of two numbers is 143. If the greater number is divided by the difference of the numbers, the quotient is 7. What is the difference of the two numbers ?
Explanation
Let the two numbers be x and y, where x is the greater number (x > y).
According to the first condition:
x + y = 143 — (Equation 1)
According to the second condition, when the greater number is divided by the difference, the quotient is 7:
x ÷ (x - y) = 7
x = 7(x - y)
x = 7x - 7y
6x = 7y
x = 7⁄6y
Substitute the value of x in Equation 1:
7⁄6y + y = 143
13⁄6y = 143
y = (143 × 6) ÷ 13
y = 11 × 6 = 66
Now, find x:
x = 143 - 66 = 77
The difference between the two numbers is:
x - y = 77 - 66 = 11.
SIMILAR QUESTIONS
When the square of the sum of two numbers are added to the square of their difference, we get 416. The difference between the square of the sum and square of the difference is 384. What are the numbers ?
If the ratio of the sum and difference of two numbers be 17 : 13, which one of the following is the ratio of the numbers ?
What is the greatest number less than 1000 which when divided respectively by 5, 7 and 9 leaves the remainders 3, 5 and 7 respectively ?