To celebrate Telugu new year my two daughters and 3 grand children came. As a pensioner I gave Rs.1000/- and asked them to devide as they like. My daudhters took Rs.115/- each and gave the balnce to my grand children.They went to a corner of the house, and after 25 minutes came and Ritwik told : we took the amount in proportion to our ages.For every Rs.7 I got, brother got Rs.6 and for every 4 brother got, sister got Rs.3/_..since you know our total age is 17 1/2 years, you tell the amounts we got and as you are forgetting everything you tell our ages also. " They gave me time upto 8 .P.M.
Answers
Answer:
AGES :
Ritwik - 7 years old
Brother - 6 years old
Sister - 4.5 years old
AMOUNT RECEIVED :
Ritwik - Rupees 308
Brother - Rupees 264
Sister - Rupees 198
Step-by-step explanation:
There are 2 daughters
They took Rs. 115 each
So totally, the daughters took 2 * 115 = Rs. 230
Remaining amount = 1000 - 230 = 770
So Rs. 770 was shared among the 3 grandchildren
Now it is given that the amounts were shared among the 3 grandchildren IN PROPORTION TO THEIR AGES
Let the age of Ritwik be x
Let the age of the brother be y
Let the age of the sister be z
For every 7 Rupees Ritwik got, brother got Rs.6
For every 4 Rupees brother got, sister got Rs. 3
So the amount got by Ritwik and brother is proportional to their ages
Age of Ritwik = x, Age of brother = y
=> ( 7/6 ) = ( x/y )
=> 7y = 6x
=> x = ( 7y/6 ) -------> Equation 1
Again, the amount got by brother and sister is proportional to their ages
Age of brother = y, Age of sister = z
=> ( 4/3 ) = ( y/z )
=> 4z = 3y
=> z = ( 3y/4 ) -----------> Equation 2
It is also given that the sum of the ages of the 3 grandchildren is 17.5
=> x + y + z = 17.5 ------------> Equation 3
Apply Equation 1 and Equation 2 in Equation 3
x = ( 7y/6 ) and z = ( 3y/4 )
=> ( 7y/6 ) + ( y ) + ( 3y/4 ) = 17.5
Taking LCM of he denominators ( LCM of 6, 1, 4 = 12)
=> ( 14y/12 ) + ( 12y/12 ) + ( 9y/12 ) = 17.5
=> ( 14y + 12y + 9y ) / ( 12 ) = 17.5
=> ( 14y + 12y + 9y ) = 17.5 * 12
=> ( 14y + 12y + 9y ) = 210
=> 35y = 210
=> y = 210/35
=> y = 6
Apply y = 6 in Equation 1
=> x = ( 7y/6 )
=> x = ( 7 * 6 ) / ( 6 )
=> x = ( 42 ) / ( 6 )
=> x = 7
Apply y = 6 in Equation 2
=> z = ( 3y/4 )
=> z = ( 3 * 6 ) / ( 4 )
=> z = ( 18 ) / ( 4 )
=> z = 4.5
Now we have calculated the ages of the 3 grandchildren
We have to calculate the amounts received by the 3 grandchildren
We know that the amounts were distributed among the 3 grandchildren IN PROPORTION TO THEIR AGES
We know that their ages are 7, 6, 4.5 respectively
So the proportion of their ages is 7 : 6 : 4.5 ( Ritwik : Brother : Sister )
Let Ritwik, brother and sister get Rupees 7a, 6a and 4.5a respectively (We have kept a as the common factor to be multiplied because the money received is proportional)
We know that the total money received by the 3 grandchildren is Rs. 770
=> 7a + 6a + 4.5a = 770
=> 17.5a = 770
=> a = ( 770 ) / ( 17.5 )
=> a = 44
Money received by Ritwik = 7a = 7 * 44 = Rs. 308
Money received by brother = 6a = 6 * 44 = Rs. 264
Money received by sister = 4.5a = 4.5 * 44 = Rs. 198