The HCF and LCM of two numbers are 11 and 7700 respectively. If one of the numbers is 275, find the other number.
Product of numbers = HCF * LCM => 275 * N2 = 11 * 7700 => N2 = 84700 / 275 = 308.
Evaluate: $\sin(30 deg) + \cos(60 deg) - \tan(45 deg)$
$\sin(30 deg) = 1/2, \cos(60 deg) = 1/2, \tan(45 deg) = 1$. Value = 1/2 + 1/2 - 1 = 0.
A man buys a cycle for Rs. 1,400 and sells it at a loss of 15%. What is the selling price of the cycle?
SP = 1400 * (1 - 0.15) = 1400 * 0.85 = Rs. 1,190.
Find the median of the following dataset: 12, 7, 15, 10, 19, 21, 5
Arranging in ascending order: 5, 7, 10, 12, 15, 19, 21. The 4th term (middle element) is 12.
If 20% of A = 30% of B = 1/6 of C, find the ratio A : B : C.
A/5 = 3B/10 = C/6. Equating to k yields A = 5k, B = 10k/3, C = 6k. Wait, 1/5 A = 3/10 B = 1/6 C. Multiply by 30: 6A = 9B = 5C => A:B:C = 5:3:6 or simplified 15:10:18.