Raju and Lalitha originally had marbles in the ratio 4 : 9. Then Lalit

Solution

Given
In this question, we are given that

• Raju and Lalitha originally had marbles in the ratio 4: 9
• Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became 5: 6

To find
We need to determine

• The fraction of her original number of marbles was given by Lalitha to Raju

Approach and Working
Let’s assume that the original marbles with Raju and Lalitha were 4m and 9m
If Lalitha gave n number of marbles to Raju, we can say

• Fraction of her original number of marbles was given by Lalitha to Raju = n/9m

As per the question given,

• (4m + n)/(9m – n) = 5/6
Simplifying, we get m/n = 11/21

Hence, n/9m = 1/9 * 21/11 = 7/33

Thus, option B is the correct answer.

Correct Answer: Option B

Let the number of marbles with Raju and Lalitha be 4x and 9x respectively.
Lalitha gives 'y' marbles to Raju.
It is given, \(\frac{{4x+y}}{{9x-y}}=\frac{5}{6}\)
So, \(\frac{y}{x}=\frac{21}{11}\)
Fraction of original marbles given by Lalitha =\(\frac{y}{9x}\)
=\(\frac{21}{11}*\frac{1}{9} =\frac{7}{33}\)

Option B

We can take the number of marbles with Raju and Lalitha as 4k and 9k.
Let’s assume Lalitha gave ‘x’ of her marbles to Raju.
As a result of this, the ratio of marbles with Raju and Lalitha is now 5:6. Let the number of marbles with Raju and Lalitha, NOW, be 5y and 6y.

Clearly,
9k – 6y = x and 4k – 5y = -x. Substituting the value of x, we have,

4k – 5y = 6y – 9k which on simplification gives 13k = 11y OR \(\frac{k}{y}\) = \(\frac{11}{13}\).

If k = 11, the number of marbles with Raju and Lalitha are 44 and 99 respectively.
If y = 13, the number of marbles with Raju and Lalitha are 65 and 78 respectively.
This means Lalitha gave 21 marbles and Raju received 21 marbles which fits in with the above sets of values.

Of 99 marbles, Lalita gave 21. The required fraction is \(\frac{21 }{ 99}\) = \(\frac{7}{33}\).

The correct answer option is B.

Hope that helps!

[quote="Bunuel"]Raju and Lalitha originally had marbles in the ratio 4 : 9. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became 5 : 6. What fraction of her original number of marbles was given by Lalitha to Raju?

A. 1/5

B. 7/33

C. 1/4

D. 1/3

E. 1/2/quote]

let x=L's gifted marbles/L's original marbles
x=(9/13-6/11)/(9/13)→
x=7/33
B

Let the original numbers of marbles with Raju and Lalitha be 4x and 9x, respectively.
Also, let y marbles were transferred from Lalitha to Raju.
Thus, after the transfer, the final number of marbles with Raju and Lalitha will be 4x+y and 9x-y, respectively.

Thus, (4x+y)/(9x-y) = 5/6
=> 24x+6y = 45x-5y
=> 21x = 11y
=> x = (11/21)y

Required fraction = 21/11*9 = 7/33

Thus, the correct option is B.

Thought of this alternate approach:
Raju:Lalitha
Ratio 1: 4:9 -> sums to 13
Ratio 2: 5:6 -> sums to 11
LCM of 13 and 11 is 143.

Multiplying Ratio 1 by 11: 44:99
Multiplying Ratio 1 by 13: 65:78
Subtracting both sides: -21 and 21

Hence, Lalitha gave 21 marbles i.e 21/99 or 7/33