Aptitude - Time and Distance - Discussion

Equation 1 : DF= 4 * t1.
Equation 2 : DB= 9 * (9-t1). As distance= speed * time.

Here let t1 be time taken by foot.
Here time taken by bicycle is (total time taken - time taken by foot).

Now equate the equation;
Now DF+DB= 4t1 + 9 * (9-t1).
Now we know DF+DB is 61.
61= 4t1+81-9t1.
61=-5t1+81.
-20=-5t1.
t1=4.

So, the Time taken by foot is 4hrs.
Now distance by foot = speed * time.
D = 4 * 4 = 16 km.

@All.

Here's my explanation.

Basically, I deduced the given information into two equations:

df = 4tf -----> (1) [ Distance = Speed x Time (Speed mentioned)]
db = 9 x (9 - tb) --->(2) (Same as above)
Where,
df = distance on foot,
tf = time taken on foot,
db = distance on a bicycle,
tb = distance on bicycle

Now, db = 61 - df, as df + db = 61 (given),
Also, tb = 9 - tf, as tf + tb = 9 (given),

So now keeping values together we get,
df = 4tf-->from (1)
61 - df = -5tf + 81 -->from (2)

Solving these two equations, we get the value of tf which comes out to be 4 hours and hence putting this value in (1) we get, df = 16km!

61km travel in 9hours.

4kmph by foot --> taken time is "x"
9kmph by bicycle --> taken time is "y"
So,

x + y = 9 ---> (1)
Distances = speed × time.
Distance by foot--> 4 × x = 4x.
Distance by bicycle--> 9 × y = 9y.
So,
4x + 9y = 61 ----> (2)

If we solve (1) & (2) equations, we can got.
y = 5
x = 4.

So;
Distance by foot = 4x,
=4 × 4.
=16km.

Very interesting, Thanks, everyone.

It's very easy.

Farmer travels - 4km/hr.
Speed = 4km/hr and Time = 4 hours.

HOW?
- Well in 1 hour he travels 1 Km, then in 4 hours he will travel 4km.

So, Distance = Speed * Time.
= 4km/hr * 4hr.
= 16km (Hr gets cancel).

Here in this question, multiple of 4 is the distance traveled. Which is 16.

Let the dist traveled on foot and bicycle be x&y.

Here total dis ie x + y = 61 ---> (1)

Also total time = 9,
So x/4 + y/9 =9,
9x+4y =324 ---> (2).

So, Eq 1 and 2 we get x =16, y = 45.

From options it will be simple to solve;

61-14 = 47,
61-15 = 46,
61-16 (Dist travelled by foot) = 45, Only this is divisible by 9.

So the answer is 16.

Note: This is applicable here only because the hours are given in terms of Integers, not in fraction.
And the answer will only be the multiple of 4.

9 hours mean 9 times. So the procedure is;

4km, 9km,
4km, 9km,
4km, 9km,
4km, 9km.

So on foot, he travelled 16 km.

Logically, if he travels x km by feet then reaming distance should be in multiples of 9 since he had travelled remaining distance with 9kmph.

Let we try from options:

A. 14 remaining distance=61-14=47 which is not multiple of 9 since get cancelled.
B. 15 remaining distance= 61-15=46 also not multiple of 9 so cancelled.
C. 16 remaining distance=61-16=45 it's multiple of 9 so we get the answer.