Advertisements
Advertisements
प्रश्न
A bus covers a distance of 90 km at a uniform speed. Had the speed been `(15"km")/"hour"` more it would have taken 30 minutes less for the journey. Find the original speed of the bus
उत्तर
Let the original speed of the bus be “x” `"km"/"hr"`
Time taken to cover 90 km = `90/x`
After increasing the speed by `(15"km")/"hr"`
Time taken to cover 90 km = `90/(x + 15)`
By the given condition
`90/x - 90/(x + 15) = 1/2`
`(90(x + 15) - 90x)/(x(x + 15)) = 1/2`
90x + 1350 – 90x = `(x^2 + 15x)/2`
1350 = `(x^2 + 15x)/2`
2700 = x2 + 5x
x2 + 15x – 2700 = 0
(x + 60) (x – 45) = 0
x + 60 = 0 or x – 45 = 0
x = – 60 or x = 45
The speed will not be negative
∴ Original speed of the bus = `(45"km")/"hr"`
APPEARS IN
संबंधित प्रश्न
Determine the quadratic equation, whose sum and product of roots are – 9, 20
Solve the following quadratic equation by factorization method
4x2 – 7x – 2 = 0
Solve the following quadratic equation by formula method
36y2 – 12ay + (a2 – b2) = 0
If the difference between a number and its reciprocal is `24/5`, find the number
A garden measuring 12m by 16m is to have a pedestrian pathway that is ‘ω’ meters wide installed all the way around so that it increases the total area to 285 m2. What is the width of the pathway?
There is a square field whose side is 10 m. A square flower bed is prepared in its centre leaving a gravel path all round the flower bed. The total cost of laying the flower bed and gravelling the path at ₹ 3 and ₹ 4 per square metre respectively is ₹ 364. Find the width of the gravel path
Determine the nature of the roots for the following quadratic equation
x2 – x – 1 = 0
Find the value of ‘k’ to identify the roots of the following equation is real and equal
(5k – 6)x2 + 2kx + 1 = 0
The roots of the equation 2x2 – 7x + 5 = 0 are α and β. Without solving for the roots, find `(alpha + 2)/(beta + 2) + (beta + 2)/(alpha + 2)`
The roots of the equation x2 + 6x – 4 = 0 are α, β. Find the quadratic equation whose roots are α2 and β2
