Given $\frac{2}{x}+\frac{2}{xy}=\frac{1}{6} and \frac{2}{x}+\frac{2}{y}=0, Find \text{'}a\text{'} for which y= ax-4.$

Mathematices

Sana and Ripa earn in the ratio 2: 1. They spend in the ratio 5: 3 and save in the ratio 4: 1. If the total monthly savings of both Sana and Ripa are Tk. 5,000, calculate the monthly income of Ripa.

Mathematices

A certain amount increases by 60% in six years at a simple interest rate. What will be the interest of Tk. 12,000 after 3 years at the same rate compounded annually?

Mathematices

In a square field of side 30 meters, 4 cows are grazing the field as they are tied at each of the four corners with a 14 meter long rope for each cow. What is the ungrazed area in the field?

Mathematices

There are two examination rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A then the number of students in A is double the number of students in B. What is the number of students in room A?

Mathematices

If m and n are whole numbers such that $m^n$ prime prime =121, then the value of (m - 1)^{(n + 1)}  is: