A can complete a piece of work in 10 days, B in 15 days and C in 20 days, A and C worked together for two days and then A was replaced by B. In how many days, altogether, work was completed?

If $$ {tan\ θ={a\over b}}$$ then $$ {a\sinθ+b\cosθ\over{a\sinθ-b\cosθ}}$$  is

Vivek buys 3 shirts at an average price of Rs. 1250. If he buys 2 more shirts at an average price of Rs. 1450. What will be the average price (in Rs.) of all the 5 shirts he buys?

The ratio of two numbers is 2: 3 and their L.C.M is 48.  What is the number?

Direction: Each of the questions consists of a question and two statements numbered I and II given below it. You have to decide whether the data provide in the statements are sufficient to answer the question. Read both the statements and Give answer.
(A) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone not sufficient to answer the question;
(B) If the data in statement II alone are sufficient to answer the question, while the data in statement I all are not sufficient to answer the question;
(C) If the data either in statement I alone or in statement II alone are sufficient to answer the question;
(D) If the data even in both statements I and II together are not sufficient to answer the question;
(E) If the data in both statements I and II together are necessary to answer the question.

What is the two-digit number?
I. Sum of two digits of number is 12 and ratio between them is 2: 1.
II. Product of two digits of number is 32 and quotient of the two digits is 2. 

Express 35% as a simple fraction:

A conical vessel whose internal radius is 12 cm and height 50 cm. is full of liquid. The contents are emptied into a cylindrical vessel with radius (internal) 10 cm. The height to which the liquid rises in the cylindrical vessel is-

Two circles having radii 5 units intersect each other in such a way that each of them passes through the centre of the other. Then the length of their common chord is