ABC is an equilateral triangle with side 12 cm and AD is the median. Find the length of GD if G is the centroid of ΔАВС.

Anil bought two articles A and B at a total cost of ₹ 10,000. He sold the article A at 15% profit and the actacle B at 10% loss. In the whole deal, be made no profit or no loss. Find the selling price of the article A.

A and B can do a piece of work in 18 days. B and C together can do it in 30 days. If A is twice as good a workman C, find in how many days B alone can do the work?

An article is listed at ₹ 7,600 and the discount offered unit is 10%. What additional discount must be given to bring the net selling price to ₹5,814?

If $${secθ+tanθ\over secθ-tanθ}=2{51\over79}$$, then the value of sinθ is equal to:

In a two-digit number, its units digit exceeds its tens digit by 2 and that the product of the given number and the sum of its digits is equal to 460. The number is:

If $${8+2\sqrt{3} \over 3\sqrt{3}+5}=a\sqrt{3}-b$$, then the value of a+b is equal to:

In a triangle, ABC, P and Q are points on AB and AC, respectively, such that AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, and CQ = 45 cm. If the area of ΔAPQ is 12 $${{cm^2}}$$, then find the area of BPQC.