## Simple Equation Solving And Logical Problems

Below given are three practice questions. First and the third require equation solving while the second one just requires logical thinking in simplifying a given phrase.

Question 1

Sylvia maintained a beautiful garden in front of her home. In the garden, Sylvia had Rose, lily, and jasmine flower pots. One day she saw bees roaming around the garden. 1/5 th of the bees went to rose pots,1/3 rd of bees went to lily pots. 3 times the difference of the above two went to the jasmine flower pots. One lone bee was flying around Sylvia’s head. She was posing a question to her friend Rathy, as how many bees were there in all. Can you answer this question to Sylvia?

(a)18 (b) 20 (c) 15 (d) cannot be determined

Solution:

Let the total number of bees be x.
Bees that went to rose pots =x/5 and bees that went to lily pots = x/3.
Bees that went to Jasmine pots =3 (x/3-x/5)
One more bee was present which was flying around Sylvia's head.
Therefore, total number of bees = x/5 + x/3 + 3(x/3-x/5) + 1 =x
x/5 + x/3 + x-3x/5 + 1=x
Multiplying the whole equation by 15,
3x + 5x + 15x - 9x + 15=15x
x=15

Question 2

Thenral Thenmozhi was pursuing mathematics in a famous college at Chennai. One day, a professor cancelled the classes saying, “Class is cancelled today on account of Sunami threat.We will meet again at 1:00 PM three days after two days before the day before tomorrow”. When exactly Thenral Thenmozhi has to attend her next class?

(a) 2 days after (b) Tomorrow (c) Same day evening (d) confusing

Solution:

3 days after 2 days before is nothing but tomorrow. The day before tomorrow of tomorrow is obviously the next day ie tomorrow.
We shall simplify the phrase "three days after two days before the day before tomorrow"
"the day before tomorrow" is nothing but today. Hence above phrase can be rewritten as
"three days after two days before today"
Calculating 3 days from 2 days before today will be nothing but tomorrow

Question 3

During Summer holidays, Deepa and Ramya visited their uncle who was residing in a village. It was a different experience in the village for these two girls. Aunty engaged them teaching how to play games with marbles.In one particular game both Ramya and Deepa had the same number of marbles when they started playing.After sometime Deepa gained 50 marbles. After some time Deepa lost 3/5 th of what she had. At the same instance Ramya had 3 times as many marbles as Deepa had. Can you find out the number of marbles the girls had at the start ?

(a) 100 (b) 200 (c) 175 (d)140

Solution:

It is stated that both Deepa and Ramya had the same number of marbles to start with. Let us assume both of them had x number of marbles when the game began. After sometime Deepa gained 50 marbles, which means she had x+50 marbles and Ramya had x-50 marbles.
Later, Deepa lost 3/5th marbles. Therefore, Deepa had (x + 50) - (3/5)( x + 50) = 2/5 (x+50)
These lost 3/5th of marbles by Deepa would had been gained by Ramya
These 2/5 (x+50) marbles would had been gained by Ramya. Therefore, she would have had x - 50 + 3/5(x + 50). At that particular instance, Ramya's marble count was thrice that of Deepa.

i.e 3 * 2 / 5(x + 50)= x - 50 + 3 / 5(x + 50)
6 / 5 (x + 50)=8/5 x - 20 or
6x+300=8x-100 (By multiplying both sides by 5)
2x= 400 or x=200
The number of marbles Deepa and Ramya had initially = 200.

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