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Bunuel
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Sonu decides to distribute 2727 apples among Tina, Mina and Dika. 10 Aug 2024, 13:45
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B
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85% (hard)

Question Stats:

56% (03:05) correct 44% (02:56) wrong based on 106 sessions

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­Sonu decides to distribute 2727 apples among Tina, Mina and Dika. He intends to distribute the apples, such that 5 times of what Tina gets, 4 times of what Mina gets and 9 times of what Dika gets are all equal. But by mistake, he distributed the apples in the ratio 4 : 3 : 2 among Tina, Mina, and Dika respectively. Due to this mistake, how many less apples did Mina get as compared to what he should have got?

A. 303
B. 306
C. 315
D. 324
E. 333
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B
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siddhantvarma
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Sonu decides to distribute 2727 apples among Tina, Mina and Dika. 13 Aug 2024, 06:36
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­First, let's find out how the apples should have been distributed.
Let's say Tina gets x apples Then, Mina gets 5x/4 apples (because 5x = 4(5x/4))
And Dika gets 5x/9 apples (because 5x = 9(5x/9))

The total number of apples: x + 5x/4 + 5x/9 = 2727 => (36x + 45x + 20x) / 36 = 2727 => 101x / 36 = 2727 => 101x = 2727 * 36 => x = (2727 * 36) / 101 = 972

So, the correct distribution should have been:
Tina: 972
Mina: 5x/4 = (5 * 972) / 4 = 1215
Dika: 5x/9 = (5 * 972) / 9 = 540

Now, let's see how the apples were distributed in the ratio 4 : 3 : 2
Total parts = 4 + 3 + 2 = 9
Tina got: (4/9) * 2727 = 1212
Mina got: (3/9) * 2727 = 909
Dika got: (2/9) * 2727 = 606

The question asks how many less apples Mina got compared to what she should have got.
ina should have got: 1215 Mina actually got: 909 Difference: 1215 - 909 = 306Therefore, Mina got 306 less apples than she should have.

The correct answer is B. 306.­
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Sonu decides to distribute 2727 apples among Tina, Mina and Dika. 16 Sep 2024, 08:32
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siddhantvarma
­First, let's find out how the apples should have been distributed.
Let's say Tina gets x apples Then, Mina gets 5x/4 apples (because 5x = 4(5x/4))
And Dika gets 5x/9 apples (because 5x = 9(5x/9))

The total number of apples: x + 5x/4 + 5x/9 = 2727 => (36x + 45x + 20x) / 36 = 2727 => 101x / 36 = 2727 => 101x = 2727 * 36 => x = (2727 * 36) / 101 = 972

So, the correct distribution should have been:
Tina: 972
Mina: 5x/4 = (5 * 972) / 4 = 1215
Dika: 5x/9 = (5 * 972) / 9 = 540

Now, let's see how the apples were distributed in the ratio 4 : 3 : 2
Total parts = 4 + 3 + 2 = 9
Tina got: (4/9) * 2727 = 1212
Mina got: (3/9) * 2727 = 909
Dika got: (2/9) * 2727 = 606

The question asks how many less apples Mina got compared to what she should have got.
ina should have got: 1215 Mina actually got: 909 Difference: 1215 - 909 = 306Therefore, Mina got 306 less apples than she should have.

The correct answer is B. 306.­
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can someone explain what happened in the first part i dont get it at all

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Sonu decides to distribute 2727 apples among Tina, Mina and Dika. 16 Sep 2024, 08:58
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Bunuel
­Sonu decides to distribute 2727 apples among Tina, Mina and Dika. He intends to distribute the apples, such that 5 times of what Tina gets, 4 times of what Mina gets and 9 times of what Dika gets are all equal. But by mistake, he distributed the apples in the ratio 4 : 3 : 2 among Tina, Mina, and Dika respectively. Due to this mistake, how many less apples did Mina get as compared to what he should have got?

A. 303
B. 306
C. 315
D. 324
E. 333
Show more

We are given that:


5T = 4M = 9D
T : M = 4 : 5 = 36 : 45
T : D = 9 : 5 = 36 : 20

Thus:


T : M : D = 36 : 45 : 20

Now, solving for the total:


36x + 45x + 20x = 2,727
x = 27


So, Mina should have received:


M = 45x = 45*27 = 1,215

However, due to the mistake, Mina actually received 3/9 of 2,727 (since the ratio was 4 : 3 : 2), which is:


3/9 of 2,727 = 909.

Therefore, the difference between what Mina should have received and what she actually got is:


1,215 - 909 = 306.

Answer: B.
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Sonu decides to distribute 2727 apples among Tina, Mina and Dika. 16 Sep 2024, 08:58
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siddhantvarma
­First, let's find out how the apples should have been distributed.
Let's say Tina gets x apples Then, Mina gets 5x/4 apples (because 5x = 4(5x/4))
And Dika gets 5x/9 apples (because 5x = 9(5x/9))

The total number of apples: x + 5x/4 + 5x/9 = 2727 => (36x + 45x + 20x) / 36 = 2727 => 101x / 36 = 2727 => 101x = 2727 * 36 => x = (2727 * 36) / 101 = 972

So, the correct distribution should have been:
Tina: 972
Mina: 5x/4 = (5 * 972) / 4 = 1215
Dika: 5x/9 = (5 * 972) / 9 = 540

Now, let's see how the apples were distributed in the ratio 4 : 3 : 2
Total parts = 4 + 3 + 2 = 9
Tina got: (4/9) * 2727 = 1212
Mina got: (3/9) * 2727 = 909
Dika got: (2/9) * 2727 = 606

The question asks how many less apples Mina got compared to what she should have got.
ina should have got: 1215 Mina actually got: 909 Difference: 1215 - 909 = 306Therefore, Mina got 306 less apples than she should have.

The correct answer is B. 306.­
can someone explain what happened in the first part i dont get it at all

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Let's break the question down step by step.
Quote:
Sonu decides to distribute 2727 apples among Tina, Mina and Dika. He intends to distribute the apples, such that 5 times of what Tina gets, 4 times of what Mina gets and 9 times of what Dika gets are all equal.
Show more
Let's say Tina gets T apples, Mina gets M apples and Dika gets D apples. From the above statement, we can say that 5*T = 4*M = 9*D
You can now find out both T and D in terms of M.
If 5*T = 4*M => T = (4*M/5)
Similarly, D = (4*M/9)
Total number of apples = 2727
We know the apples are distributed amongst only the three people, so if we add T + M + D we should get the total number of apples.
So we can write this as: T + M + D = 2727
Substitute the values of T and D in terms of M that we calculated earlier from;
(4*M/5) + M + (4*M/9) = 2727
The above is a linear equation in one variable, M so we can solve it to get the value of M which comes out to be 1215.
1215 is the number of apples Mina should have got.

Okay now lets' come to the second part of the question:
Quote:
But by mistake, he distributed the apples in the ratio 4 : 3 : 2 among Tina, Mina, and Dika respectively.
Show more
We now have the ratio of the number of apples Tina, Mina and Dika actually got. From this, we can simply calculate how many apples Mina got:
4x + 3x + 2x = 2727 => 9x = 2727 => x = 303
Number of apples Mina got: 3x => 3*303 => 909
Hence, 909 is the number of apples Mina actually got.

Now the final part of the question:
Quote:
Due to this mistake, how many less apples did Mina get as compared to what he should have got?
Show more
From the above we can say Mina got 1215 - 909 = 306 apples less, which is what we're asked. Hope it's clear now!
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