THREE FRIENDS PLUCKED SOME MANGOES FROM A MANGO GROVE AND COLLECTED THEM TOGETHER IN A PILE AND TOOK A SMALL NAP AFTER THAT.AFTER SOME TIME 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 FREIND GOT UP NOT KNOWING WHAT HAPPENED AND DIVIDED THE REST OF THE MANGOES INTO THREE EQUAL PARTS. THERE WAS ONE MANGO EXTRA. HE GAVE IT TO A MONKEY NEARBY, TOOK ONE SHARE FOR HIMSELF AND WENT TO SLEEP AGAIN.NEXT THE THIRD FREIND GOT UP NOT AWARE OF WHAT HAD HAPPENED AND DIVIDED THE MANOGOES INTO THREE EQUAL SHARES. THERE WAS THIS TIME TOO ONE MANGO EXTRA. HE GAVE IT TO A MONKEY NEARBY, 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 FREINDS PLUCK INITIALLY? ALSO EXPLIAN THE PROCCESS.
let the number of initial mangoes be 3x+1
after first distrubution, i.e. x+x+x+1, and giving x to the boy and 1 to the monkey. 2x remain
In second distribution, giving 1 to the monkry, 2x-1 remain. dividing it equally into 3 parts = (2x-1)/3 parts each.So, after giving one part to guy, remain mangoes = 2(2x-1)/3
In third distribution, giving one to the monkey and divinding it by 3 and equating two parts to 30
as follows, (((2(2x-1)/3)-1)/3 )* 2 = 30
((4x-2)/3 - 1 )/3 ) * 2 = 30
(4x-5 )*2/9 = 30
4x- 4 = 135
x = 35
So, the total amount of mangoes = (35 *3 ) + 1 = 106