Question
If a, 1, b are in arithmetic progression and 1, a, b are
in geometric progression, then a and b are respectively equate to _______ (where a ≠b).Solution
Given a, 1, and b are in AP and 1, a, and b are in GP: From AP= 1- a=b-1 b=2- a  … (1) From GP- b = a²    … (2) from Eq (1) and Eq (2) a² = 2-a a²+a-2=0 a2+2a- a -2 =0 a = 1 or - 2 Since a ≠1: a = -2 b = a² = 4 So, a = -2 and b = 4. Alternate method- According to the option- (a + b)/2 = 1 (a + b) = 2 Put the value of a and b in the option and satisfied. Taking option 2. (-2 + 4) = 2 2 = 2 (satisfied)
If the difference of two numbers is 4 and the difference of their squares is 56, then the larger number is
The product of two positive numbers is 432. If one number is three times the other, find the difference between the two numbers.
A man spends 1/7 of his income on food, 3/5 of his income house rent and 1/4 of his income on clothes. If he still has Rs. 200 left with him, his income...
- If '57x8y' is a five-digit number which is divisible by 72, then find the value of (5x - y).
- A number exceeds its square root by 30. What is the number?
- A two-digit number has digits summing up to 10. On subtracting 36 from the number, the digits get interchanged. What is the original number?
The sum of two numbers is 60 whereas the sum of their reciprocals is (20/9). Find the square of the product of the two numbers.
- When a number is divided by 60, the remainder is 17. What will be the remainder when the same number is divided by 10?
Consider a three-digit number where the middle digit (tens place) is 3. If the digits in the hundreds and ones places are swapped, the new number become...
- What should be subtracted from 1200873 to make it divisible completely by 6?
Relevant for Exams:
