# Question 7 & 8

**Question 7: One hundred cats can eat 100 mice in 100 days time, then in how many days four cats will eat four mice ?**

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**Solution:**

This is a situation of direct and indirect proportion i-e as the days increase, more cats require more mice and few cats will require more mice, and more cats will finish eating more mice in few days.

Formula here is ;

**So, 4 cats will also require 100 days to eat 4 mice !**

**Question 8: A man completes a 10 hour journey. He travels 21 km/h in the first half of the journey and at rate of 24 km/h in second half. Find the total kilometers of the journey.**

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**Solution: **

Here the technique of distance formula is to be used. Distance is calculated by multiplying speed with time taken. Here we have to calculate the distance.

Let the total distance is ‘x+y’ Kms from point A to C!

Let distance covered from point A to B in first half i-e in 5 hours is X kms and distance covered from B to C in second half i-e next 5 hours is Y kms

**Case 1 – Distance for First Half (5 hours) :**

We are given that in first half he travels with speed of 21 kms per hour.

We know Distance = Speed x Time

i-e

S is distance, V is speed and T is time; Put values of S, V and T in the relation, we get;

Here,

S= X, V=21 km/h and T=5 hours

**Case 2 – Distance For second half ( Next 5 hours):**

We use same formula. Here Time is again 5 hours, but for second half speed will be 24 kms per hour.

Here,

S= Y, V=24 km/h and T=5 hours

**So, total distance is X+Y i-e 105+120 = 225 kms **