Question
Three numbers are given such that when the average of
any two numbers is added to the third number, the resulting sums are 450, 420, and 400. Determine the difference between the largest and smallest numbers.Solution
ATQ,
Let the numbers be A, B, and C. Given: (A + B)/2 + C = 450 → A + B + 2C = 900 (B + C)/2 + A = 420 → B + C + 2A = 840 (C + A)/2 + B = 400 → C + A + 2B = 800 Add all three equations: A + B + 2C B + C + 2A C + A + 2B = 900 + 840 + 800 = 2540 4A + 4B + 4C = 2540 A + B + C = 635 From A + B + C = 635: Use A + B + 2C = 900 (635 - C) + 2C = 900 → C = 265 Use A + C + 2B = 800 (635 - B) + 2B = 800 → B = 165 A = 635 - B - C = 635 - 165 - 265 = 205 Final values: A = 205 B = 165 C = 265 Difference between largest and smallest: 265 - 165 = 100
- Which prominent figure was among the early leaders of the Prarthana Samaj movement?
Where was the 2024 Indo-Pacific Chiefs of Defence (IP-CHOD) Conference held?
Which Hindi weekly newspaper was started by Pandit Madan Mohan Malaviya in 1907?
Which Indian city is also known as the "Pink City"?Â
Where was the Special Session of the G7 Ministers' Meeting on Culture held in September 2024?
Who is the chairperson of the working group for the revision of WPI base year and transition to PPI?
India's Shipping Ministry has approved waterway projects worth ₹645 crore on Brahmaputra river in which state?
- Which article of the Indian Constitution stipulates that courts shall not examine the proceedings of State Legislatures?
'Mycorrhiza' is a symbiotic association between:
Consider the following statements about nanotechnology:
1. It involves manipulating materials at the atomic and molecular scale.
2. Nanote...