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Inheritance Related Calculations Based On the Quran

By Naseer Ahmed, New Age Islam

19 August 2015

There are only three main verses relating to inheritance based on which books have been written to cover all possible situations which number 200 or more. Imagine the Quran containing say 200 verses covering each distinct case of inheritance alone! The Quran covers the subject in three verses and these three verses are both necessary and sufficient to cover every possibility. However, it requires us to know some basic school level arithmetic covering fractions and proportions and nothing more. It is not at all surprising however, that there are very few who have even such rudimentary knowledge of arithmetic because of which they blame God that He does not know His arithmetic!

The three verses are:

(4:11) Allah (thus) directs you as regards your Children´s (Inheritance): to the male, a portion equal to that of two females: if only daughters, two or more, their share is two-thirds of the inheritance; if only one, her share is a half. For parents, a sixth share of the inheritance to each, if the deceased left children; if no children, and the parents are the (only) heirs, the mother has a third; if the deceased Left brothers (or sisters) the mother has a sixth. (The distribution in all cases (´s) after the payment of legacies and debts. Ye know not whether your parents or your children are nearest to you in benefit. These are settled portions ordained by Allah; and Allah is All-knowing, Al-wise.

From 4:11 above, we deduce that siblings of the deceased inherit only in the absence of child of the deceased. The presence or absence of parents of the deceased has no effect.

(12) In what your wives leave, your share is a half, if they leave no child; but if they leave a child, ye get a fourth; after payment of legacies and debts. In what ye leave, their share is a fourth, if ye leave no child; but if ye leave a child, they get an eighth; after payment of legacies and debts. If the man or woman whose inheritance is in question, has left neither ascendants nor descendants, but has left a brother or a sister, each one of the two gets a sixth; but if more than two, they share in a third; after payment of legacies and debts; so that no loss is caused (to any one). Thus is it ordained by Allah; and Allah is All-knowing, Most Forbearing.

The Arabic word Kalala has been translated as “without ascendants and descendants”. My view is that it means without descendants alone since we have seen in 4:11 that siblings inherit when parents of the deceased are survivors but not when a descendant or child of the deceased is a survivor. The same applies for the word Kalala used in 4:176 below.

(176) They ask thee for a legal decision. Say: Allah directs (thus) about those who leave no descendants or ascendants as heirs. If it is a man that dies, leaving a sister but no child, she shall have half the inheritance: If (such a deceased was) a woman, who left no child, Her brother takes her inheritance: If there are two sisters, they shall have two-thirds of the inheritance (between them): if there are brothers and sisters, (they share), the male having twice the share of the female. Thus doth Allah make clear to you (His law), lest ye err. And Allah hath knowledge of all things.

The brother/sister in 4:12 is understood to be uterine brother/sister meaning having a common mother but different father. Otherwise, 4:176 would appear to contradict 4:12. Also, uterine siblings can inherit only in the absence of descendants and siblings from common father.

The division starts after all debts of the deceased are settled including outstanding Mehar (if any) and one year maintenance of his wife or wives and the legacies or the will of the deceased if he has left a will.

The deceased leaves assets in the form of property, cash, jewellery etc. All assets can be valued and it is the value that is divided and each inheritor can then choose in what form he will take his share of the value. What cannot be divided can then be sold and converted to cash or the excess/shortfall settled in cash. For example, if a property is worth Rs 40 lacs and a person’s inheritance is determined as Rs 30 lacs, he could still choose to take the property by paying Rs 10 lacs which will be used to settle the inheritance of the rest. This person will then obviously not take anything from the Jewellery and other assets because he has taken the full value of his inheritance from the property alone.

Let us work through a few examples to understand the principle of distribution enunciated in the Quran.

A couple of points can be stated upfront: A son (or a brother in the absence of descendants), always inherit as residuary or what is left after those with fixed fractions are given their share. In the presence of a son, the daughter inherits as a residuary. In the absence of a son, the daughter(s) inherit as residuary if what remains after those with fixed proportions get their share is less than the maximum fixed share of the daughter(s) or as inheritor with fixed fraction if what remains is more than their maximum fixed share. The same goes for a sister with/without brother.

When there are residuary, the maximum residuary is 1 or 100% and the minimum residuary is after reducing the share of spouse, and both parents. If the deceased is a male, then the minimum residuary is (1-(1/8+1/6+1/6))= 13/24

If the deceased is a female, then the minimum residuary is (1-(1/4+1/6+1/6)) =5/12

So there is never a problem about distribution when there is a residuary meaning either a son or a brother in the absence of a child or children.

When there is no residuary (neither a son or brother) and only inheritors with fixed fractions, then it goes without saying that the fixed fractions will in general not add upto 1. Such a case is dealt with by treating the fractions as relative proportions for the distribution.

For example, if a person is survived by only parents and no children or spouse or siblings, then the fathers fixed share is 1/6 and mother’s 1/3, Since there are no other inheritors, the fractions will be treated as proportions and the father and mother will inherit in the proportion 1/6:1/3 or  1/6:2/6 or 1:2 and the father will inherit 1/3 and the mother 2/3.The calculation follows simple rules of logic and arithmetic and there is no flaw in the Quran. Those who talk about arithmetical flaw in the Quran are poor in logic and arithmetic.

In general, when there is no residuary as inheritor, treat the fractions as the relative proportion for distribution.

Now take the case when a person is survived by both parents and one daughter only. Each of the parent’s share is then 1/6 and the daughters is ½ or less. Now since the residuary after each of the parents get 1/6 is 2/3 which is more than ½, the daughter’s share will also be treated as a fixed fraction. They will therefore inherit in the ratio 1/6:1/6:1/2 0r 1:1:3. The father gets 1/5, the mother 1/5 and the daughter 3/5. Notice that each one gets more than the fixed fraction because the fixed fractions add upto less than 1. However the final distribution is in accordance with the law since the proportion of each inheritor is maintained.

Take the case of the deceased survived by both parents and 2 daughters. The fixed share of two or more daughters is 2/3 or less. Since after the parents are given their share of 1/6 each, what remains is exactly 2/3, the two sisters will share this equally or each one gets 1/3. This is a rare case when the fixed fractions add upto 1. If we solve this problem with proportions also we get the same result as may be expected.  The proportions now are: 1/6:1/6:2/3 = 1:1:4 The father therefore gets 1/6, mother 1/6 and each of the two sisters get 2/6 (=1/3).

Let us now take the case of a person survived by his wife, both parents and 2 daughters.

What remains after the wife gets her share of 1/8 and each parent 1/6 is (1-(1/8+1/6+1/6)) = 13/24 which is less than 2/3. The daughters will now inherit as residuary and each one will get 13/48.

Now consider the case where the deceased is survived by only one parent and two daughters.

The proportions now are 1/6:2/3 or 1:4 The parent gets 1/5 and each of the two daughters get 2/5

The calculations with son/brother as residuary are shown below:

Let us say a man is survived by a son and daughter only (no spouse, parents or grandparents).

The son gets 2/3 and the daughter 1/3.

In general, if there are x sons and y daughters only, then the share of each son is 2/(2x+y) and the share of each daughter = 1/(2x+y). If the sons and daughters are residuary then the share of each son = (residual fraction)*2/(2x+y) and the share of each daughter = (residual fraction)*1/(2x+y)

Now let us take the case where a man is survived by spouse, both parents and a son and a daughter.

The wife gets her fixed share of 1/8 and each of the parents 1/6, leaving a residual of 13/24 which is distributed among the son and the daughter in the ratio 2:1 or the son gets 2/3*(13/24) = 26/72 and the daughter 13/72.

The share of the son and daughter in the residue could also have been calculated using the formula: Share of each son = (residual fraction)*2/(2x+y) and the share of each daughter = (residual fraction)*1/(2x+y), where x and y are the number of sons and daughters respectively. In this case, since x and y are both 1, the share of son = 13/24*(2/(2*1+1) )= 26/72 and the share of the daughter = 13/24*(1/3)=13/72

Let us consider a controversial case. Let us say a deceased is survived by only daughter and sister (no parents, spouse or brother).

According to 4:11, if only daughter, her share is ½ and according to 4:176, if only single sister without brother her share is ½. So do the daughter and sister inherit ½ each? Remember that siblings inherit only in the absence of descendants and the daughter is a descendant. Siblings cannot inherit when there are descendants. The daughter therefore inherits 100%. Most Muftis are likely to not allow a daughter more than ½ as per 4:11 which is clearly incorrect.

With the help of the examples worked out above, the methodology has been made clear and you should now be able to work out any case.

All the above rules derive logically from the Quran. If the Quran was to explicitly cover each and every situation, a separate chapter with 200 verses would have been required just to cover each distinct case of inheritance since the number of combinations of inheritors in the absence of a male who is a residuary run into more than 200.

Read a book on inheritance and try to cover the same in three verses and then you will be able to appreciate the beauty of these verses which succinctly cover every case but require us to use rules of logic and arithmetic.

Disclaimer: You can trust our Ulema to muddy the clearest of waters. This subject is more amenable for muddying than any other subject because very few understand it in any case. You will therefore find variations depending upon the various schools of jurisprudence. I have not followed any school but directly derived the rules from the three verses in the Quran and rules of logic and arithmetic.

Naseer Ahmed is an Engineering graduate from IIT Kanpur and is an independent IT consultant after having served in both the Public and Private sector in responsible positions for over three decades. He is a frequent contributor to