Radhika got first price in sports championship of her school so her parents bought cake. That day she eats ½ of the cake. On the next day, she eats 1/3 of the remaining cake, on the third day she eats ¼ and fourth 1/5, fifth day 1/6, on the sixth day she eats 1/7th of what is remaining and so on…..
If her elder brother also joins on 5th day and eats and he eats the cake twice of what Radhika had, then what fraction of cake is left. *
1 point
7/10
1/10
5/6
3/5
What would be the fraction of cake available on 7th day? *
1 point
7/10
1/70
5/7
1/56
If after 4th day cake gets spoil, how much of cake is still available? *
1 point
0.25
1234/2345
1/5
0.12345
plz say right answer plz do not mistake i trust u my brainlist
Answers
Solution :-
Let us assume that, her parents bought (2 * 3 * 4 * 5 * 6 * 7) 5040 gm of cake for radhika .
So,
→ First day she ate = (1/2) * 5040 = 2520 gm of cake .
→ Left cake after 1st day = 2520 gm .
Now,
→ 2nd day she ate = (1/3) * 2520 = 840 gm of cake .
→ Left cake after 2nd day = 2520 - 840 = 1680 gm .
and,
→ Third day she ate = (1/4) * 1680 = 420 gm of cake
→ Left cake after 3rd day = 1680 - 420 = 1260 gm .
again,
→ Fourth day she ate = (1/5) * 1260 = 252 gm of cake
→ Left cake after 4th day = 1260 - 252 = 1008 gm .
Now, When cake spoil after 4th day .
→ Cake still available = 1008/5040 = 1/5 (c) (Ans.)
Now,
→ Cake for 5th day = 1008 gm
→ Radhika ate = (1/6) * 1008 = 168 gm
→ Radhika's elder brother ate = 2 * (1/6) * 1008 = 2 * 168 = 336 gm
then,
→ Cake left after 5th day = 1008 - (168 + 336) = 504 gm
therefore,
→ Required fraction of cake left = 504/5040 = (1/10) (b)
Now,
→ 6th day she ate = (1/7) * 504 = 72 gm of cake
→ Left cake after 6th day = 504 - 72 = 432 gm .
therefore,
→ Fraction of cake available on 7th day = 432/5040 = (72 * 6)/(72 * 70) = (6/70) = (3/35)
also, if we assume his brother didnt join on 5th day ,
→ Cake for 5th day = 1008 gm
→ Radhika ate = (1/6) * 1008 = 168 gm
So,
→ Cake left after 5th day = 1008 - 168 = 840 gm
now,
→ Cake for 6th day = 840 gm
→ Radhika ate = (1/7) * 840 = 120 gm
So,
→ Cake left after 6th day = 840 - 120 = 720 gm
therefore,
→ Fraction of cake available on 7th day = 720/5040 = 72/504 = (72)/(7 * 72) = (1/7)
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