Find the number of positive integral solutions to x + y + $z = 10$.
Number of positive integer solutions to $x_{1}$ + ... + $x_r$ = n is C(n-1, r-1). Here $n=10$, r=3 => C(9, 2) = 36.
In a competitive exam, 4 marks are awarded for every correct answer and 1 mark is deducted for every wrong answer. A student attempted 80 questions and scored 220 marks. How many questions did he answer correctly?
Let C be correct questions. 4C - 1(80 - C) = 220 => 5C - 80 = 220 => 5C = 300 => $C = 60$.
The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, find the second number.
Ratio A:B:C = (2*5) : (3*5) : (3*8) = 10 : 15 : 24. Sum of parts = 49. Second number $B = (15 / 49) \cdot 98 = 30$.
A trader sells two items at Rs. 990 each. On one he gains 10% and on the other he loses 10%. What is his overall gain or loss percentage?
When selling price is same and % gain = % loss = r, overall result is loss of (r/10)^2 = (10/10)^2 = 1% loss.
A machine depreciates in value at the rate of 10% per annum. If its present value is Rs. 1,62,000, what was its value 2 years ago in rupees?
$P * (0.90)^2 = 162000 => P * 0.81 = 162000 => P = 200,000.$