Question

for a harvest festival, a fruit merchant bought 280 apples , 50 orange and 385 pears he made identical gift basket containing all the three varieties of food what is the largest number of identical baskets he can make what is the maximum number of each fruit that he can keep in each basket ? with formula

Answer 1

Here we have to find the H.C.F. of 50 , 280 ,385

By Euclid's division lemma :-
Let c=50 b=280and a =385
Let us take a and b

a =bq+r where a>b

385=280×1+105
280=105×2+70
105=70×1+35
70=35×2+0

remainder comes 0 so the H.C.F. of 385 and 280 is 35 . Let 35 =d

Now let us take d and c

c=dq+r. where c>d

50=35×1+15
35=15×2+5
15=5×3+0

Here the remainder comes 0 so the H.C.F of 50 , 280 and 385 is 5 .

So the maximum number of basket will be 5 .

Number of fruits in 1 basket :-
apples =280÷5=56
oranges=50÷5=10
pears=385÷5=77

So 56 apples , 10 oranges and 77 pears can be accommodated in 1 basket .

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