A number N consists of two digits. The digit in the tens place is 3 times the digit in the units place. The digits are reversed and the resulting number is denoted by R. If \( N \times R = 3627 \), then what is the product of the digits of the number N?
A boatman can row to a place (Y) at a distance of 24 km from the starting point (X) and back in 14 hours. If he can row 4 km with the stream in the same time as 3 km against it, what is the speed of the stream?
An alloy (X) of gold and silver is taken in the ratio 1 : 2 and another alloy (Y) of gold and silver is taken in the ratio 2 : 3. How many parts of X and Y must be taken to obtain a new alloy Z consisting of gold and silver in the ratio 4 : 7?
N is a 3-digit number. The middle digit of N is equal to the sum of the other two digits and the sum of the digits is 10. How many such numbers (N) can be possible?
The ratio of the cost price of two articles X and Y is 1 : 2. A businessman earns a profit of p% by selling X and a loss of 3p% by selling Y. If he loses 20% in this transaction, then what is the value of p?
A sum of money at the rate of 5% per annum compounded annually becomes n times in 100 years. What is the value of n?
(Given \( \log_{10} 2 = 0.301 \), \( \log_{10} 3 = 0.477 \) and \( \log_{10} 7 = 0.845 \))
A variable y is directly proportional to a variable quantity \( x^{n} \). Given that when x = 2, y = 20.8 and when x = 3, y = 105.3. Which one of the following is the constant of proportionality if it is greater than 1?
