Three friends plucked some mangoes from a mango grove and collected them together in a pile and took nap after that.After sometime, one of the friends woke up and divided the mangoes into three equal numbers. There was one mango extra. He gave it to a monkey nearby, took one part for himself and
slept again. Next the second friend got up unaware of what has happened,
divided the rest of the mangoes into three equal shares. There was an extra
mango. He gave it to the monkey, took one share for himself and slept
again. Next the third friend got up not knowing what happened and divided
the mangoes into three equal shares. There was an extra mango. He gave it
to the monkey, took one share for himself and went to sleep again. After
some time, all of them got up together to find 30 mangoes. How many
mangoes did the friends pluck initially?
Answers
Answer:
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Step-by-step explanation:
Given :
A boy runs for 10 min at a uniform speed of 9km/hr and 20 min at average speed of 12km/hr
To Find :
Speed the boy will take in next 20 min = ?
Solution :
We know,
\sf{}Average\ Speed=\dfrac{Total\ Distance}{Total\ Time}Average Speed=Total TimeTotal Distance
Total time => 10 + 20 = 30min
Convert minute into hour. [1h= 60min,so 1min = 1/60h]
Thus, total time in min = 30/60
\sf{}\implies 12=\dfrac{Toatl\ distance}{\frac{30}{60}}⟹12=6030Toatl distance
\sf{}\implies 12\times \dfrac{30}{60}=Total\ distance⟹12×6030=Total distance
\sf{}\therefore Total\ distance=6km∴Total distance=6km
Therefore,total distance is equal 6m
Distance covered in 10min/distance which boy walk earlier) :-
We know,
\sf{}Speed=\dfrac{Distance}{Time}Speed=TimeDistance
Covert 10 min into hr
=> 10/60hour
\sf{}\implies 9=\dfrac{Distance}{\frac{10}{60}}⟹9=6010Distance
\sf{}\implies 9\times \dfrac{10}{60}=Distance⟹9×6010=Distance
\sf{}Distance=1.5kmDistance=1.5km
Then remaining distance,
\sf{}\bf{}Remaing\ distance=Total\ distance-distance\ travelled\ earlierRemaing distance=Total distance−distance travelled earlier
\sf{}\implies 6-1.5⟹6−1.5
\sf{}\therefore 4.5km∴4.5km
Therefore,for next 20 the boy should run with a speed,
\sf{}Speed=\dfrac{Distance}{Time}Speed=TimeDistance
Covert 20min into hr
=> 20/60hr
\sf{}Speed=\dfrac{4.5}{\frac{20}{60}}Speed=60204.5
\sf{}\implies \dfrac{4.5}{\frac{2}{6}}⟹624.5
\sf{}\implies \dfrac{4.5}{\frac{1}{3}}⟹314.5
\sf{}\implies 4.5\div \dfrac{1}{3}⟹4.5÷31
\sf{}\implies 4.5\ \times 3⟹4.5 ×3
\sf{}\therefore 13.5km/h∴13.5km/h
Therefore,speed needed for next 20min is equal to 13.km/h