The sum of two numbers is 40 and their difference is 4. What is the product of the numbers?
396
Let the two numbers be \(x\) and \(y\) with \(x>y\). We are given \(x+y=40\) and \(x-y=4\).
Add the two equations: \((x+y)+(x-y)=40+4\), so \(2x=44\) and \(x=22\).
Subtract to find the other number: \(y=40-22=18\).
The product is \(22 \times 18 = 396\).
Hence, the product of the numbers is 396.
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Important Questions from Linear Equation in 2 or more Variables
Six years ago, the ratio of ages of A to B was 7 ∶ 5. After 4 years from now, the ratio of their ages will be 11 ∶ 9. What is A’s age at present?
7p - [3q - {8p - (4q - 10p)}] = ?
Surya is 25 years older than his son. In 5 years, he will be twice as old as his son. What will be Surya’s age after 3 years?
The difference between the ages of two sisters is 2 years when father’s age is 52. Father is elder by 2 years to mother. Elder sister’s age is half of mother’s age. Find the age of younger sister?
The sum of the digits of a 2 digit number is 9, When 27 is added to the number, the digits get interchanged. Find the number.
A. 45
B. 36
C. 18
D. 27
