Solution: (c)

Ratio of the work done by Sujit and Amit = 80 : 100 = 4 : 5

Total key depressions done by Amit = \(\displaystyle \frac{5}{9}\times 576000=320000\)

Amit’s speed in key depressions per hour = \(\displaystyle \frac{{320000}}{{8\times 5}}=8000\)

Alternate method:

Let Amit’s speed of key depressions per hour be X.

So, Sumit’s speed of key depressions is 80% of X.

In total, the number of key depressions per hour by both of them is 1.8 X

The total number of key depressions in a day by both of them together is 1.8 \(\displaystyle \times \)8 X= 14.4 X

This equals 576000/5 = 115200.

So, 14.4 \(\displaystyle \times \) X = 115200

or, X = 115200/14.4 = 8000

Solution: (d)

Distance covered by the aeroplane in 9 h = \(\displaystyle 9\times 756=6804km\)

Speed of helicopter = \(\displaystyle \frac{{2\times 6804}}{{48}}=283.5km/h\)

Distance covered by helicopter in 18 h = \(\displaystyle 283.5\times 18=5103km\)

Solution: (c)

Let each wheel make x revolutions per sec. Then,

\(\displaystyle [(2\pi \times \frac{7}{2}\times x)+(2\pi \times 7\times x)]\times 10=1980\)

\(\displaystyle (\frac{{22}}{7}\times 7\times x)+(2\times \frac{{22}}{7}\times 7\times x)=198\)

 66x = 198 \(\displaystyle \Rightarrow \) x = 3.

Distance moved by smaller wheel in 3 revolutions

\(\displaystyle (2\times \frac{{22}}{7}\times \frac{7}{2}\times 3)cm/\sec =66cm/\sec \)

Solution: (b)

Let the usual speed of the aeroplane be x km/h.

Then, \(\displaystyle \frac{{1500}}{x}-\frac{1}{2}=\frac{{1500}}{{(x+250)}}\)

\(\displaystyle \frac{{1500}}{x}-\frac{{1500}}{{x+250}}=\frac{1}{2}\Rightarrow \frac{{1500x+75000-1500x}}{{x(x+250)}}=\frac{1}{2}\)

\(\displaystyle 750000={{x}^{2}}+250xor{{x}^{2}}+250x-750000=0\)

\(\displaystyle {{x}^{2}}+1000x-750x-75000=0\)

 (x + 1000) (x – 750) = 0 \(\displaystyle \Rightarrow \) x = 750, – 1000

Speed cannot be negative

We get x = 750 km/h

Solution: (b)

Then, distance travelled by bicycle = (61 –x) km

So, \(\displaystyle \frac{x}{4}+\frac{{61-x}}{9}=9\)

\(\displaystyle 9x+4(61-x)=9\times 36\)

9x – 4x = 324 – 244

5x = 80

x = 16 km