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Q.

Bhavani has three daughters: Seema, Reshma, and Krishna. Bhavani gives a total of Rs. 2,016 as a monthly allowance to her daughters, such that Krishna gets 1 2   of what Seema gets and Reshma gets 1 2 3  times Krishna’s share. Then the amount of money each of them received individually are


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a

864, 720, 432

b

864, 721, 432

c

864, 720, 435

d

820, 720, 432 

answer is A.

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Detailed Solution

Given, Bhavani has three daughters: Seema, Reshma, and Krishna. Bhavani gives a total of Rs. 2,016 as a monthly allowance to her daughters, such that Krishna gets 1 2   of what Seema gets and Reshma gets 1 2 3  times Krishna’s share.
Total amount = Rs. 2,016
Let the amount received by Seema, Reshma, Krishna be x, y, and z respectively.
Then, Krishna’s share = 1 2 ×  Seema’s share
⇒   z= 1 2 ×x   ⋯⋯⋯(1)  
Reshma’s share = 1 2 3   ×   Krishna’s share
⇒   y=1 2 3 ×z= (1×3)+2 3 ×z= 5 3 z   ⋯⋯⋯(2)  
Substitute (1) in (2):  ⇒   y= 5 3 z= 5 3 × 1 2 ×x= 5 6 x   ⋯⋯⋯(3)  
From equations (1), (2), (3), the total amount can be expressed as:
Total amount = x+y+z=x+ 5 6 x+ 1 2 x  
= 1 1 x+ 5 6 x+ 1 2 x  
The L.C.M. of 1,6,2 is 6.
Therefore,
1 1 x+ 5 6 x+ 1 2 x= 1×6 1×6 x+ 5×1 6×1 x+ 1×3 2×3 x = 6 6 x+ 5 6 x+ 3 6 x = 6+5+3 6 x = 14 6 x  
So,
  2016= 14 6 x ⇒x=2016÷ 14 6 =2016× 6 14 =864  
i.e., x=864  .
Then,
y= 5 6 x= 5 6 ×864 =720  
z= 1 2 x= 1 2 ×864 =432  .
Hence, the amount of money Seema, Reshma, Krishna received are Rs.864, Rs.720, Rs.432 respectively.
Hence, the correct option is 1.
 
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