Question
A man is 6 times as old as his daughter. After 4 years,
he will be 4 times as old as she will be. After how many more years will the man be 3 times as old as his daughter?Solution
Let the daughter's present age be x years. Then the man's present age is 6x years. After 4 years, the man's age will be 6x + 4, and the daughter's age will be x + 4. Given: 6x + 4 = 4(x + 4). 6x + 4 = 4x + 16. 2x = 12 → x = 6 years. So, the man's current age is 6 * 6 = 36 years. Let y years later, the man’s age will be 3 times the daughter’s age. 36 + y = 3(6 + y). 36 + y = 18 + 3y. 2y = 18 → y = 9 years.
42, 54, 78, 114, 168, 222
What will be come in place of (?) in the given number series.
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24, 13, ?, 29, 117, 937
If cos A = 4/5 and A is an acute angle, find the value of 3 tan A + 4 sec A.
