Three numbers are such that if the average of any two of them is added to the third number, the sums obtained are 168, 174 and 180 respectively. What is the average of the original three numbers?

The least number, which must be added to 6709 to make it exactly divisible by 9, is 

Simplify : $$\sqrt{[(12.1)^2-(8.1)^2]÷[(0.25)^2+(0.25)(19.95)]} $$

A person invested some amount at the rate of 12 % simple interest and a certain amount at the rate of 10 % simple interest for 1 year. He received yearly interest of Rs. ₹ 130, but if he had interchanged the amount invested, he would have received 4 more as interest. How much did he invest at 12 % simple interest? 

The perimeter of a rectangle and equilateral triangle is equal. One side of the rectangle is also equal to the side of the triangle. Find the ratio of the areas of the rectangle and triangle?

Six years ago, the ratio of the ages of the two persons P and Q was 3:2. Four years hence the ratio of their ages will be 8:7. What is P’s age?

Directions:  In the following two equations questions numbered (I) and (II) are given. You have to solve both equations and
Give answer
(a) If x > y
(b) If x ≥ y
(c) If y > x
(d) If y ≥ x
(e) If x = y or no relation can be established

$$ {I.x^{2}=81}$$
$$ {II.(y-9)^{2}}=0$$

A sum of money lent out at simple interest amounts to ₹720 after 2 years and 1020 after a further period of 5 years. Find the principal.