A single discount which is equivalent to a series of discounts \( p\% \), \( \frac{p}{2}\% \), \( \frac{p}{4}\% \) is 31.6%. What is the value of \( p \)?
A locomotive engine can go 40 km/hr. Its speed gets reduced by a quantity that varies directly as the square root of the number of wagons attached. It is known that its speed becomes 16 km/hr if 36 wagons are attached. What is the smallest number of wagons with which the engine is unable to move?
Two numbers P and Q are such that P : Q = x : y. If 1 is added to both the numbers, the ratio becomes 7 : 10. If 3 is added to both the numbers, the ratio becomes 3 : 4. What is \( (x + y) : (x - y) \) equal to?
ABC is a triangle right-angled at C. A semicircle is drawn on AB as diameter. Let P be any point on AC produced such that AP = AB = 10 cm. Further, B and P are joined. If BC = 8 cm, then what is BP equal to?
All possible groups of 3 distinct numbers from among A, B, C, D and E are formed. If the aggregate of sums of numbers of each group is 120, then what is the arithmetic mean of A, B, C, D and E?
The sum of the deviations of a set of \( n \) numbers \( x_{1}, x_{2}, x_{3}, \ldots, x_{n} \) measured from 15 is -90 and the sum of the deviations of the same numbers measured from -3 is 54. What is the arithmetic mean?
The numbers 59, 53, 51, 43, 36, \( (8x + 1) \), \( (x^{2} + 1) \), 13, 12, 9, 7, 3 are written in descending order and their median is 25. What is/are the values of \( x \)?
