This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
31. The sum of two numbers is 14. Their difference is 10. The product of the two numbers is Step 1: Set up equations for the given information. Let the two numbers be x and y. The sum of the two numbers is 14: x + y = 14 (1) The difference of the two numbers is 10: x - y = 10 (2) Step 2: Solve the system of equations to find the values of x and y. Add equation (1) and equation (2): (x + y) + (x - y) = 14 + 10 2x = 24 x = (24)/(2) x = 12 Substitute the value of x into equation (1): 12 + y = 14 y = 14 - 12 y = 2 Step 3: Calculate the product of the two numbers. Product = x · y Product = 12 · 2 Product = 24 The correct option is B. B) 24 32. Which of the following States will not be heading to Legislative Assembly polls in April/May 2026? To determine which state will not have Legislative Assembly polls in April/May 2026, we need to consider the typical 5-year term for state assemblies and when the last elections were held for each state: • Tamil Nadu: Last assembly elections were held in April 2021. The next elections are expected in April/May 2026. • Assam: Last assembly elections were held in March-April 2021. The next elections are expected in March-April 2026. • Kerala: Last assembly elections were held in April 2021. The next elections are expected in April/May 2026. • Punjab: Last assembly elections were held in February 2022. The next elections are expected in February/March 2027. Based on these schedules, Punjab will not be heading to Legislative Assembly polls in April/May 2026, as its next elections are due in 2027. The correct option is D. D) Punjab