Question
Six years ago from now, age of 'A' was ____ years.
Ratio of present ages of 'A' and 'B' is ____ respectively and four years hence from now, sum of ages of 'A' and 'B' will be ____ years. The data given in which among the given options will fill the blank in the same order so as to make the statement true? I. 18, 2:3, 68 II. 21, 3:5, 82 III. 22, 4:5, 75Solution
Statement I:
Present age of 'A' = 18 + 6 = 24 years
Present age of 'B' = (3/2) × 24 = 36 years
Required sum = 24 + 4 + 36 + 4 = 68 years
So, statement I is true. Statement II:
Present age of 'A' = 21 + 6 = 27 years
Present age of 'B' = (5/3) × 27 = 45 years
Required sum = 27 + 4 + 45 + 4 = 80 years
So, statement II is not true. Statement III:
Present age of 'A' = 22 + 6 = 28 years
Present age of 'B' = (5/4) × 28 = 35 years
Required sum = 28 + 4 + 35 + 4 = 71 years
So, statement III is not true. Therefore, only statement I is true. Hence, option E .
What is the simplified value of the given expression?
4(sin² 20° + sin² 70°) + 2sin 30° - (2sec 60° + cot 45°)
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