Question
"The monthly incomes of Amit and
Bhuvan are in the ratio of 8:5. Bhuvan's monthly expenditure is 70% higher than Amit's monthly savings. Amit's monthly expenditure exceeds Bhuvan's by Rs. 7,800. If their monthly savings are in the ratio of 5:4, what is the average monthly income of Amit and Bhuvan?"Solution
ATQ, Let the monthly savings of Amit and Bhuvan are Rs. 5p and Rs. 4p respectively. Monthly expenditure of Bhuvan = 1.7 × 5p = Rs. 8.5p Monthly expenditure of Amit = Rs. 8.5p + 7800 According to question: (5p + 8.5p + 7800)/ (4p + 8.5p) = 8/5 67.5p + 39000 = 100p 32.5p = 39000 p = 1200 So, the monthly income of Amit = 5 × 1200 + 8.5 × 1200 + 7800 = 6000 + 10200 + 7800 = Rs. 24,000 Monthly income of Bhuvan = 4 × 1200 + 8.5 × 1200 = 4800 + 10200 = Rs. 15,000 So, the average monthly income of Amit and Bhuvan = (24000 + 15000)/2 = 39000/2 = Rs. 19,500
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 24x + 143 = 0
Equation 2: y² - 20y + 96 = 0
l. 3x2 + 17x + 24 = 0
II. 2y2 + 15y + 27 = 0
I. x2 – 3(x + 5) = -11
II. y2 – 4(y + 2) = -2y
I. 8a2 – 22a+ 15 = 0
II. 12b2 - 47b + 40=0
If α, β are the roots of the equation x² – px + q = 0, then the value of α2+β2+2αβ is
...I. 2y2 + 11y + 15 = 0
II. 3x2 + 4x - 4= 0
I. 3p² + 13p + 14 = 0
II. 8q² + 26q + 21 = 0
- Suppose both the roots of q² + kq + 49 = 0 are real and equal, then determine the value of 'k'.
I. x2 – 18x + 81 = 0
II. y2 – 3y - 28 = 0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 34x + 285 = 0
Equation 2: y² - 26y + 165 = 0
