Question

An ant moved for several seconds and covered $3$ mm in the first second and $4$ mm more in each successive second than in its predecessor.If the any had covered $1$ mm in first second and $8$ m more in each successive second, then the difference between the path it would cover during the same time and the actual path would be more than $6$ mm but less than $30$ mm. Find the time for which the ant moved (in seconds)

• A. $5s$
• B. $4s$
• C. $6s$
• D. None of these

Answer 1

Answer: (B)

$4s$

Let ant move for t second

Case I: $S_t$ when ant move 3 m min first second and 4 m min in each second.

$S_n=\frac{t}{2}\left[2\right(3)+(t-1\left)4\right]$

Case II: $S_t$ when ant move 1 mm in first second and 8 mm in each second

$S_t=\frac{t}{2}\left[2\right(v)+(t-1\left)8\right]$

ATQ

$6<\frac{t}{2}[2+(t-1\left)8\right]-\frac{t}{2}[6+(t-1\left)4\right]<30$

$6<\frac{t}{2}[-8+4t]<30$

$6<[-4t+2t^2]<30$

From option putting t=4 Only condition is satisfied

$6<-16+32<30$

$6<16<30$