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Hari(H), Gita(G), Irfan(I) and Saira(S) are siblings (i.e., brothers and sisters). All were born on $1^{\text{st}}$ January. The age difference between any two successive siblings (that is born one after another) is less than three years. Given the following facts:

1. Hari's age $+$ Gita's age $>$ Irfan's age $+$ Saira's age
2. The age difference between Gita and Saira is one year. However Gita is not the oldest and Saira is not the youngest.
3. There are no twins.

In what order they were born (oldest first)?

1. $\text{HSIG}$
2. $\text{SGHI}$
3. $\text{IGSH}$
4. $\text{IHSG}$

if option B is correct i.e SGHI

S                            G                              H                         I

1st jan 2010            1st jan 2011               1st jan 2012          1st jan 2013

Their Age as of 1st jan 2019

9 yrs                        8 yrs                          7 yrs                     6 yrs

Hari's age + Gita's age > Irfan's age + Saira's age

7             + 8              = 6              + 9

15 = 15

Here  their sum are equal and not greater as mentioned in question.

Note that the given information is not sufficient for finding the exact order of birth of the given 4 children. There are multiple possible order which will satisfy this criteria.

You may substitute the actual values which satisfies the formulae that you have derived from the given information. But it is not meaningful to do the reverse, i.e. choosing any values without considering whether they satisfy all of the given information or not.

@ This combination doesn’t work, try some other combination having a successive age difference of 2. example, take SGHI=12,11,8,5

Given that,

• $H+G > S+I$
• No twins,
• And either $G=S+1$ or $S = G+1$
• $G$ is not the oldest and $S$ is not the youngest.

Lets analyze each case,

Case 1:

$G=S+1$,

It implies, $H > I - 1$, Since twins are not possible $H>I$

Case 2:

$G = S - 1$,

It implies $H > I + 1$

Therefore, both cases imply $H$ is older than $I,$ also $G$ and $S$ must be placed successively.

Only option B satisfies these implications.

I can't understand case (i). What does the twins exactly mean?

Twin means having same age (here).

No twins means no जुड़वाँ ( no body has same age).

Case i: G = S+1

=>H + G > S+ i

=>H + S + 1> S +i   (putting G value)

=>H + 1 >i (cancelling S of both side)

=> H> i-1

Case ii) G = S-1

H + G> S + i

H + S -1> S + i

H -1 > i

H > i +1

Correct answer is B. Though, its a hit-n-trial method.

option A: There is no such possibility, as it is given that there are no twins, so S and G must be consecutive.

option B.For some combination of ages of SGHI we can satisfy (1) condition like taking ages as, S=5 G=5 H=3 I=1, (2) and (3) are also satisfied. So, all the 3 conditions are satisfied.

option C: IGSH, so I > G and S > H (as there are no twins) and so I + S > G + H - violates condition 1.

option D: IHSG, so I > H and S > G and so I + S > H + G - violates condition 1.

I have a question, how can you take S and G equal ? their diff. is 1 @ujjwal saini
This comment should've been best answer..

@amolagrawal The max. difference can be 2 since in question,

The age difference between any two successive siblings (that is born one after another) is less than three years.

see ,if this approach helps

According to me, option “c” should be the answer.

Reason-    Hari's age + Gita's age > Irfan's age + Saira's age   (given)  ---------1

saira’s age – gita’s age=1   (given) ---------2

from (1)     hari – irfaan > saira – gita

hari – irfaan >1     (from 2)

hence only option C satisfies this

@ correct me if anything is wrong

by