If a3 = 117 + b3 and a = 3 + b, then the value of a + b is:
a3 – b3 = 117 and a – b = 3 ⇒ a3 – b3 = (a – b) (a2 + b2 +ab) ⇒ 117 = 3 (a2 + b2 +ab) ⇒ 39 = a2 + b2 +ab ⇒ a2 + b2 = 39 – ab we Know that (a-b)² = a2 +b² - 2ab = (a-b)² = 39 – ab – 2ab = (a-b)² = 39 – 3ab 9 = 39 – 3ab = ab = 10 Now use (a+b)² = a2 + b2 + 2ab (a+b)² = 39 – ab + 2ab (a+b)² = 39 + ab = 39 + 10 (a+b)² = 49 = a + b = ±7
Average age of A, B and C is 20 years. Average age of B and C was 12 years when A was born. If B is 21 years old, then, find the age of C, 6 years hence.
The average age of 27 children and their teacher's age are 23 years. If the teacher's age is excluded, the average reduces by 1. What is the teacher's age?
A bag contains 20 rupees note, 50 rupees note and 100 rupees note in the ratio 5:7:2. If the total amount in the bag is Rs 2,600, find the average numbe...
The average score obtained by 28 students in a class test is 68 marks. The top place was shared by 3 people who got the same score. If the lowest score ...
The average age of 32 children and their teacher's age are 28 years. If the teacher's age is excluded, the average reduces by 1. What is the teacher's age?
The average of 41 consecutive odd numbers is 49. What is the largest number.
The average of 10 numbers is 21.8. The average of the last four numbers is 15. If the average of the first five numbers is 23, then what is the value of...
5 positive numbers are written on a piece of paper. Sum of first 3 numbers is 40 and ratio of the 4th and the 5th number is 2:3. If difference between t...
The average cost of 3 chairs is Rs. 9500. The average cost decrease by 15% when one more chair is included. What is the cost price of the 4th...
The average age of 23 children and their teacher's age are 21 years. If the teacher's age is excluded, the average reduces by 1. What is the teacher's age?