Correct Answer - Option 2 : 72 km
Given:
When Sita goes to a multiplex at 6 km/hr slower than her usual speed she reaches 8 minutes late
And when she goes to the multiplex at 4 km/h more speed than her usual speed she reaches 9/2 minutes early
Formula used:
Distance = Speed × Time
Calculation:
Let be distance = x km and real speed = y km/hr
Accordingly,
\(\frac{x}{{y - 6}} - \frac{x}{y} = \frac{8}{{60}}\)
⇒ 15 × (xy - xy + 6x) = 2y(y - 6)
⇒ y(y - 6) = 45x ----(1)
Again, for the 2nd case
\(\frac{x}{y} - \frac{x}{{y + 4}} = \frac{9}{{2 × 60}}\)
⇒ 40 × (xy + 4x - xy) = 3y(y + 4)
⇒ 3y(y+4) = 160x ----(2)
Dividing equation (1) by equation (2) get,
\(\frac{{y - 6}}{{3\left( {y + 4} \right)}} = \frac{9}{{32}}\)
⇒ 27y + 108 = 32y - 192
⇒ 5y = 300
⇒ y = 60
Putting this value in equation (1) get,
45x = (60 × 54)
⇒ x = \(60 × \frac{{54}}{{45}}\)
⇒ x = 72
∴ Required distance is 72 km.
