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Q.Rekha and Kallu have a certain number of red and black marbles with them. The ratio of red marbles to black marbles with them is 7 : 1 and 9 : 1 respectively. If the total number of marbles with the two persons is 90, what can be the number of red marbles with Kallu?
a.Either 9 or 45  b.Either 10 or 50  c.Either 36 or 72  d.Either 18 or 36
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My approach is to eliminate the wrong options and thus finding the correct option.

We have to find the number of red marbles Kallu have.

As Kallu having red marbles and black marbles in a ratio 9:1

So, Kallu have 9x red marbles.

Now the 1st option: 

a.Either 9 or 45

∴ 9x = 9 or 45

∴ x = 1 or 5

∴ Kallu having a total of 10x = 10 or 50 marbles

Total marbles with Rekha will be 80 or 40  [80 or 40 both can be divided in ratio 7:1]

Now the 2nd option

b.Either 10 or 50

∴ 9x = 10 or 50

this can't be possible since the value of x isn't natural.

3rd option

c.Either 36 or 72

∴ 9x = 36 or 72

∴ x = 4 or 8

∴ Kallu having a total of 10x = 40 or 80 marbles

So, Rekha having total of 50 or 10 marbles [ 50 or 10 can't be divided into 7:1 ratio]

This option is eliminated.

4th option

d.Either 18 or 36

∴ 9x = 18 or 36

∴ x = 2 or 4

∴ Kallu having a total of 10x = 20 or 40 marbles

And, Rekha will be having a total of 70 or 50 marbles  [ Both 70 or 50 can't be divided into ratio 7:1 ]

This option is also eliminated.

∴ Option a) 9 or 45 is the correct one.

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