Wheels of diameters 7 cm and 14 cm start rolling simultaneously from X and Y, which are 1980 cm apart… · ABC26GN4576
Subject: General Aptitude · Chapter: Area · Exam: M.A.T. 2005
Wheels of diameters 7 cm and 14 cm start rolling simultaneously from $X$ and $Y$, which are 1980 cm apart, towards each other in opposite directions. Both of them make the same number of revolutions per second. If both of them meet after 10 seconds, the speed of the smaller wheel is
(a)22 cm/sec
(b)44 cm/sec
(c)66 cm/sec
(d)132 cm/sec
Answer
Answer (as printed): A
Explanation
Let each wheel make $x$ revolutions per sec. Then, $\left[\left(2 \pi \times \frac{7}{2} \times x\right)+(2 \pi \times 7 \times x)\right] \times 10=1980$ $$\begin{aligned} & \Leftrightarrow\left(\frac{22}{7} \times 7 \times x\right)+\left(2 \times \frac{22}{7} \times 7 \times x\right)=198 \\ & \Leftrightarrow 66 x=198 \Leftrightarrow x=3 . \end{aligned}$$ Distance moved by smaller wheel in 3 revolutions $$=\left(2 \times \frac{22}{7} \times \frac{7}{2} \times 3\right) \mathrm{cm}=66 \mathrm{cm} .$$ ∴ Speed of smaller wheel $=\frac{66}{3} \mathrm{cm} / \mathrm{s}=22 \mathrm{cm} / \mathrm{s}$.