Que 35: Present ages of Mukti and Shakti are in the ratio 5:6, respectively. Ages of Neeti and Kriti after three years will be in the ratio of 12:7, respectively. Present average age of Mukti, Shakti and Kriti is 28 years. Find the present age of Shakti if the present average age of Mukti, Neeti and Kriti is 27 years.
Answers
Step-by-step explanation:
Given :-
Present ages of Mukti and Shakti are in the ratio 5:6, respectively. Ages of Neeti and Kriti after three years will be in the ratio of 12:7, respectively. Present average age of Mukti, Shakti and Kriti is 28 years.
To find :-
Find the present age of Shakti if the present average age of Mukti, Neeti and Kriti is 27 years?
Solution :-
Given that
The ratio of the present ages of Mukti and Shakti = 5:6
Let they be 5x and 6x years respectively.
Let the present ages of Mukti and Shakti are denoted by M and S respectively
Let the present age of Mukti (M)
(M) = 5x years
Let the present age of Shakti (S)
(S) = 6x years
The ratio of the ages after 3 years of Neeti and Kriti = 12:7
Let they be 12y and 7y years respectively
Let the present ages of Neeti and Kriti are denoted by N and K
Let the present age of Neeti (N)
(N) = (12y-3) years
Let the present age of Kriti (K)
(K) = (7y-3) years
Given that
Present average age of Mukti, Shakti and Kriti = 28 years.
We know that
Average = Sum of all observations/Number of all observations
=> Average = (M+S+K)/3
=> 28 = (5x+6x+7y-3)/3
=> 28 = (11x+7y-3)/3
=> 28×3 = 11x+7y-3
=> 84 = 11x+7y-3
=> 84+3 = 11x+7y
=> 11x+7y = 87 ---------(1)
and
The present average age of Mukti, Neeti and Kriti = 27 years.
=> Average = (M+N+K)/3
=> 27 = (5x+12y-3+7y-3)/3
=> 27 = (5x+19y-6)/3
=> 27×3 = 5x+19y-6
=> 81 = 5x+19y-6
=> 81+6 = 5x+19y
=> 5x+19y = 87 -----------(2)
On multiplying (1) with 5 then it becomes
=> 55x+35y = 435 -------(3)
On multiplying (2) with 11 then it becomes
=> 55x+209y = 957 -------(4)
On Subtracting (3) from (4) then
55x+209y = 957
55x+35y = 435
(-) (-) (-)
_______________
0 + 174y = 522
_______________
=> 174y = 522
=> y = 522/174
=> y = 3 years
On Substituting the value of y in (1) then
=> 11x+7(3) = 87
=> 11x +21 = 87
=> 11x = 87-21
=> 11x = 66
=> x = 66/11
=> x = 6 years
We have , x = 6 and y = 3
Now,
Present age of Shakti = 6x years
=> S= 6(6) years
S = 36 years
Answer:-
The present age of Shakti = 36 years
Check:-
If x = 6 and y = 3 then
Present age of Mukti
M= 5(6)
M= 30 years
Present age of Shakti
S= 6(6)
S = 36 years
Present age of Neeti
N = 12(3)-3
N = 36-3
N = 33 years
Present age of Kriti
K = 7(3)-3
K = 21-3
K = 18years
Average age of Mukti ,Shakti and Kriti
= (30+36+18)/3
= 84/3
Average of M, S and K= 28 years
and
Average age of Mukti, Neeti and Kriti
= ( 30+33+18)/3
= 81/3
Average of M,N and K = 27 years
Verified the given relations in the given problem.
Used formulae:-
Average = Sum of all observations/Number of all observations
Used Method:-
→ Substitution method
Answer:
Step-by-step explanation: