Aptitude Discussion

Q. |
Wheel of diameter 7cm 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 same number of revolutions per second. If both of them meet after 10 s, the speed of the smaller wheel is: |

✖ A. |
22 cm/s |

✖ B. |
44 cm/s |

✔ C. |
66 cm/s |

✖ D. |
88 cm/s |

**Solution:**

Option(**C**) is correct

Circumference of the smaller wheel ($X$) = $2\times \pi \times 3.5=22$ m

Circumference of the bigger wheel ($Y$) = $2\times \pi \times7=44$ m

Let both the wheels make $x$ revolutions in one second

Distance covered by both the wheel in 1 second = $22x+44x= 66x$

Distance covered by both wheels in 10 second = $660x$

Given, $660 x=1980$

$⇒ x=3$

Speed of smaller wheel = $22x=22\times 3$

= **66 cm/s**

**Bhagyashree Das**

*()
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Alternative Method:

Ratio of the speeds say s1 (smaller wheel) and s2 (bigger wheel)= Ratio of the distance covered by them, ie,

s1:s2 = 2*pie*radius of smaller wheel : 2*pie*radius of bigger wheel

ie, s1:s2 = 7:14 or 1:2

And, they meet in 10s ie

Distance between them/ Relative Speed = Time at which they meet

=>1980/ s1+s2 = 10

=> 198= x + 2x

=> 198 = 3x

=>66 =x

Thus, smaller wheel's speed is 66cm/s.