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

Question

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

Are You Up For the Challenge: 700 Level Questions

Show Answer

Official Answer

B

A. 1/5

B. 7/33

C. 1/4

D. 1/3

E. 1/2

Are You Up For the Challenge: 700 Level Questions

CareerGeek · Answer

Let the original marbles of Raju & Lalitha = 4k & 9k respectively

Then Lalitha gave some of her marbles to Raju
--> Let the marbles now of Raju and Lalitha = 4k + n and 9k - n
-->  \frac{4k + n}{9k - n} = \frac{5}{6} 
-->  24k + 6n = 45k - 5n 
-->  11n = 21k 
-->  \frac{n}{k} = \frac{21}{11}

Fraction of marbles given by Lalitha =  \frac{n}{9k} = \frac{1}{9}*\frac{21}{11} = \frac{7}{33}

Option B

preetamsaha · Answer

Let the number of marbles with Raju and Lalitha initially be 4x and 9x. 
Let the number of marbles that Lalitha gave to Raju be y.
It has been given that (4x+y)/(9x-y) = 5/6
24x + 6y = 45x – 5y
11y = 21x
y/x = 21/11
Fraction of original marbles given to Raju by Lalitha = y/9x (As Lalitha had 9x marbles initially).
y/9x = 21/99
= 7/33.

CORRECT ANSWER IS B

EgmatQuantExpert · Answer

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

mchandra · Answer

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

CrackverbalGMAT · Answer

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!

gracie · Answer

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

Are You Up For the Challenge: 700 Level Questions

Show Answer

Official Answer

B

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

GmatPoint · Answer

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.

JhonnyMe · Answer

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

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards