Question
Amit and Ben started a partnership by investing Rs.3600
and Rs.4500, respectively. Amit's investment period is 'x' months, while Ben's investment period is '(x + 3)' months. The combined profit earned by them is Rs.4100. Additionally, one-third of the difference between Amit's and Ben's profit shares is Rs.300. If Amit's share of the profit is less than Ben's, determine the duration of Ben's investment period.Solution
ATQ, Difference between the profit obtained by Amit and Ben = 300 × 3 = Rs.900 Profit obtained by Amit = (4100 – 900)/2 = 3200/2 = Rs.1600 Profit obtained by Ben = 4100 – 1600 = Rs.2500 (3600 × x)/(4500 × (x + 3)) = 16/25 4x/(5 × (x + 3)) = 16/25 x/(x + 3) = 4/5 5x = 4x + 12 x = 12 months Therefore, the Investment period of Ben will be = 12 + 3 = 15 months
I. 15y2 + 4y – 4 = 0
II. 15x2 + x – 6 = 0
- For what value of a does the quadratic equation x² + ax + 81 = 0 have real and identical roots?
I. 15b2 + 26b + 8 = 0
II. 20a2 + 7a - 6 = 0
I. x2 – 12x + 32 = 0
II. y2 + y - 20 = 0
I. 6y2 - 17y + 12 = 0
II. 15x2 - 38x + 24 = 0
I. 4x2 – 53x – 105 = 0
II. 3y2 – 25y + 48 = 0
I. 9/(4 )p + 7/8p = 21/12
II. 7/5p = 9/10q + 1/4
I. 20y² - 13y + 2 = 0
II. 6x² - 25x + 14 = 0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: 3x² + 6x - 9 = 0
Equation 2: 2y² - 16y + 32 = 0
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