When usha was thrice as old as nisha, her sister asha was 25. When nisha was half as old as asha, then usha was 34 . If ther ages add up to 100. How old is usha?
Answers
Answer:
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Step-by-step explanation:
the difference of all ages must be same
25-2a=n-a=3n-34
We will get two equation
2n+a=34
n+a=25
From the equation we will get n=9 and a=16
The ages are Asha=2a=32 Nisha =16 and Usha =34
Sum of the ages =100
(32+x)+(16+x)+(34+x)=100
82+3x=100
3x=18
x=6
Age of Usha =34+6=40
GIVEN
State1: Usha's age =3x, Nisha's age=x, Asha's age=25
State2: let after some years "t"
Usha's age =3x+t, Nisha's age=x+t, Asha's age=25+t
condition1: 3x+t+x+t+25+t=100 On solving gives 4x+3t=75----------->eq1 condition2: 3x+t=34 ------------------->eq2
condition3: x+t=1//2(25+t) On solving gives 2x+t=25---------->eq3
solve eq2 & eq3 then we get x= 9
Case1: If you substitue "x"' value in eq2 or eq3 we get t=7
Usha's age=34, Nisha's age =16, Asha's age= 32
their sum= 82 is not equal to 100
Case2: If you substitue "x"' value in eq1 we get t=13
Usha's age=40, Nisha's age =22, Asha's age= 38
their sum= 100 satisfies given condition
Therefore, Usha's age is 40