The annual incomes of two persons are in the ratio 9:7 and their expenses are in the ratio 4:3. If each of them saves INR 2000 per year, what is the difference in their annual incomes

Let ABC and A'B'C be two triangles in which AB>A'B, BC>B'C' and CA>C'A'. Let D, E and F be the mid-points of the sides BC, CA and AB respectively. Let D', E' and F' be the midpoints of the sides B'C', C'A' and A'B' respectively. Consider the following statements:

Statement I :

AD>A'D', BE>B'E' and CF> C'F' are always true.

Statement II:

AB²+BC²+CA²/AD²+BE²+CF²

=A'B'²+B'C'²+C'A'²/A'D'²+B'E'²+C'F'²

Which one of the following is correct in respect of the above statements

If a sum of money at a certain rate of simple interest per year doubles in 5 years and at a different rate of simple interest per year becomes three times in 12 years, then the difference in the two rates of simple interest per year is

A cyclist moves non-stop from A to B, a distance of 14 km, at a certain average speed. If his average speed reduces by 1 km per hour, he takes 20 minutes more to cover the same distance. The original average speed of the cyclist is

(sin 35⁰/cos55⁰)2-(cos55⁰/sin35⁰)² +2 sin 30⁰ is equal to

Let a two-digit number be k times the sum of its digits. If the number formed by interchanging the digits is m times the sum of the digits, then the value of m is