Mathematics
If the sum of two natural numbers is 27 and their product is 182, then the smaller number is :
13
14
16
18
Answer
Let two natural numbers be x and y.
Given,
Sum of numbers = 27
⇒ x + y = 27
⇒ y = 27 - x ………(1)
Given,
Product of numbers is 182.
⇒ xy = 182 ………(2)
Substituting value of y from equation (1) in equation (2), we get :
⇒ x(27 - x) = 182
⇒ 27x - x2 = 182
⇒ x2 - 27x + 182 = 0
⇒ x2 - 13x - 14x + 182 = 0
⇒ x(x - 13) - 14(x - 13) = 0
⇒ (x - 14)(x - 13) = 0
⇒ (x - 14) = 0 or (x - 13) = 0 [Using zero-product rule]
⇒ x = 14 or x = 13.
Substituting value of x in equation (1), we get :
If x = 14, y = 27 − 14 = 13
If x = 13, y = 27 − 13 = 14.
The smallest number among two numbers is 13.
Hence, option 1 is the correct option.
Related Questions
A bus covers a distance of 240 km at a uniform speed. Due to heavy rain, its speed gets reduced by 10 km/hr and as such it takes two hours longer to cover the total distance. Assuming the uniform speed to be x km/hr, form an equation and solve it to evaluate x.
A man covers a distance of 100 km, traveling with a uniform speed of x km/hr. Had the speed been 5 km/hr more, it would have taken 1 hour less. Find x, the original speed.
The sum of the squares of two consecutive odd natural numbers is 74. The greater number is :
5
7
9
none of these
Two natural numbers differ by 2 and the sum of their squares is 202. The sum of the numbers is :
14
16
18
20