Question : A cyclist, after cycling a distance of 70 km on the second day, finds that the ratio of distance covered by him on the first two days is 4 : 5. If he travels a distance of 42 km on the third day, then the ratio of distance travelled on the third day and the first day is:
Option 1: 4 : 3
Option 2: 3 : 2
Option 3: 3 : 4
Option 4: 2 : 3
Correct Answer: 3 : 4
Solution :
Let $x$ km be the distance travelled on the first day.
Distance travelled on the second day = 70 km
The ratio of distances covered by him on the first two days is 4 : 5.
$⇒\frac{x}{70}=\frac{4}{5}$
$\therefore x=\frac{4}{5}×70$ = 56 km
If he travels a distance of 42 km on the third day, then the ratio of distance travelled on the third day and the first day would be 42 : 56 = 3 : 4
Hence, the correct answer is 3 : 4.
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