It is not possible for Mr. A to claim any such deduction. It is so because only deduction allowed from house property income are Municipal taxes & 30% standard deduction.
Here is relevant section for your reference:
Deductions from income from house property.
24. Income chargeable under the head “Income from house property” shall be computed after making the following deductions, namely:—
(a) a sum equal to thirty per cent of the annual value;
(b) where the property has been acquired, constructed, repaired, renewed or reconstructed with borrowed capital, the amount of any interest payable on such capital:
Provided that in respect of property referred to in sub-section (2) of section 23, the amount of deduction shall not exceed thirty thousand rupees :
Provided further that where the property referred to in the first proviso is acquired or constructed with capital borrowed on or after the 1st day of April, 1999 and such acquisition or construction is completed 50 [within three years from the end of the financial year in which capital was borrowed], the amount of deduction under this clause shall not exceed one lakh fifty thousand rupees.
Explanation.—Where the property has been acquired or constructed with borrowed capital, the interest, if any, payable on such capital borrowed for the period prior to the previous year in which the property has been acquired or constructed, as reduced by any part thereof allowed as deduction under any other provision of this Act, shall be deducted under this clause in equal instalments for the said previous year and for each of the four immediately succeeding previous years:]
[Provided also that no deduction shall be made under the second proviso unless the assessee furnishes a certificate, from the person to whom any interest is payable on the capital borrowed, specifying the amount of interest payable by the assessee for the purpose of such acquisition or construction of the property, or, conversion of the whole or any part of the capital borrowed which remains to be repaid as a new loan.
Explanation.—For the purposes of this proviso, the expression “new loan” means the whole or any part of a loan taken by the assessee subsequent to the capital borrowed, for the purpose of repayment of such capital.]
As you can see there is no express provision for any other deduction no deduction other than above can be claimed.
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