The sum of two numbers is 156 and their HCF is 26. Find how many such pairs can be formed.
If HCF of two numbers is 26, then the two numbers are 26X & 26Y where X & Y are co-prime numbers. ⇒ H.C.F(X,Y) = 1 Now the sum of the two numbers is 156. So we can say, 26X + 26Y = 156 ⇒ X + Y = 6 The possible pairs of X & Y are: (1, 5), (2, 4), (3, 3), (5, 1), (4, 2) [As we are not considering the ordered pairs (2, 4), (4, 2), (3, 3) because X and Y are coprime] Accepted possible pairs of X & Y are: (1, 5), (5, 1) Such a number of pairs, For (1, 5) => 26, (26 × 5) = 130 For (5, 1) => (26 × 5) = 130, 26 Combining the above results, So, there will be only one pair of numbers which will give the sum of two numbers is 156 and their HCF is 16 and that pair of the numbers will be (26, 130) only.
There are 3 natural numbers. If the average of any 2 numbers is added with the third number 34, 30 and 28 will be obtained. Find the numbers.
The sum of four consecutive counting numbers is 154. Find the smallest number?
A waiter income consist of his salary and tips. During one week his tips were 4/5 of his salary. What portion of his income came from tips?
Find the number of Digits required to write down the number of Pages in a 500 page book?
In a class, 2/5 of the students are girls and rest are boys. If 4/9 of the girls and 1/3 of the boys are absent, what part of the total number of studen...
Find the average of first 24 whole numbers.
What is the average of first 24 multiples of 2.4?
Sum of two digits of a two digit number is 11. When digits of the number are reversed then number formed is 45 more than the original number. Find the ...
Find the fourth proportional to 2, 3, 6.
A number 254786ab is completely divisible by 40, What is maximum value of a and b?