Remi earns a profit of 20% on selling an article at a certain price. If she sells the articles for ₹8 more, she will gain 30%. What is the original cost price of 16 such articles?

If 27(x+y)³ – 8(x-y)³=(x+5y)(Ax²+By²+Cxy), then what is the value of (A+B-C)?

The height of a solid cylinder is 30 cm and the diameter of its base is 10 cm. Two identical conical holes each of radius 5 cm and height 12 cm are drilled out. What is the surface area (in cm²) of the remaining solid?

In ∆ABC, the bisector of ∠A intersects side BC at D. If AB = 12 cm, AC = 15 cm and BC= 18 cm, then the length of BD is:

The sum of the present ages of a father and son is 52 years. Four years hence, the son's age will be $${1\over 4}$$that of the father. What will be the ratio of the ages of the son and father, 10 years from now?

A can do a piece of work in 15 days. B is 25% more efficient than A, and C is 40% more efficient than B. A and C work together for 3 days and then C leaves. A and B together will complete the work in:

A and B are solutions of acid and water. The ratio of water and acid in A and B are 4 : 5 and 1 : 2, respectively. If x literes of A is mixed with y litres of B, then the ratio of water and acid in the mixture becomes 8 : 13. What is x : y ?

In ∆ABC, ∠A=90⁰ , AD is the bisector of ∠A meeting BC at D, and DE ⊥ AC at E. if AB = 10 cm and AC = 15 cm, then the length of DE, in cm, is: