For what value of m will the system of equations 17x+my+102=0 and 23x+299y+138=0 have infinite number of solutions? 

From an observation tower ‘h’ meter above the level of river, the angle of depression of a point on the near shore is A^° and that of a point directly on the far shore is B^°. Find the width of the river.

Simplification the following equations shown below

What is the value of sin² 60° + cos²30°+ cot² 45° + sec² 60° – cosec² 30° + cos² 0°.

Directions :- Read the given information carefully and answer the following questions.

There are four hostels i.e. A, B, C and D.

In hostel A: Number of boys are 120 and number of girls are 30% more than that of number of girls in

hostel B.

In hostel B: Number of boys are double than that of number of girls.

In hostel C: Number of boys are 100 more than that of boys in hostel A and total boys and girls in C is 1000.

In hostel D: Number of boys is 182 more than the number of boys in hostel A. Average of number of girls of hostel A and that of hostel D is 223.Number of boys in hostel D is 98 less that of boys in hostel B.

Find ratio of total number of boys and girls together in hostel B to that of in hostel C?

If a shopkeeper bought 70 kg of potatoes for Rs 420 and sold the entire purchase at the rate of 6.50 per kg, what was his profit percentage?

The product of two positive numbers is 11520 and their quotient is $$9\over5$$.Find the difference of two numbers?

The cost price of an article is ₹390. If it is to be sold at a profit of 3.12 %, how much would be its approximate selling price?