Bharti, RJD chief Lalu Prasad Yadav's daughter, had appeared before the central probe agency yesterday and was grilled for about eight hours.
Kumar, who was summoned again today after he skipped the first date on Monday, will be confronted with the documents seized by the ED in the case and the statements given by his wife in relation to their finances and business transactions, officials said on the condition of anonymity.
The agency is expected to record his statement under the Prevention of Money Laundering Act (PMLA).
Kumar, like his wife, will be questioned about his role in a firm, Ms Mishail Printers and Packers Private Limited, his other finances and his links with a chartered accountant arrested by the agency earlier in the case, they said.
The ED had on July 8 conducted searches at three Delhi farmhouses of Bharti, Kumar and the firm.
The raids had come a day after the CBI had raided multiple premises of Prasad and his family in a corruption case probe.
The latest summons to Bharti and her husband are related to a Rs 8,000 crore money laundering probe being conducted by the agency against two Delhi-based businessmen brothers, Surendra Kumar Jain and Virendra Jain, and others who are alleged to have laundered several crore rupees using over 90 shell companies.
The Jain brothers were arrested by the ED earlier under PMLA.
One of the firms that the arrested duo dealt with was Ms Mishail Printers and Packers Private Limited.
Bharti and her husband are alleged to have been directors of this firm in the past.
According to ED officials, it was detected that 1,20,000 shares of M/s Mishail Printers and Packers Private Limited were bought during 2007-08 at a rate of Rs 100 per share by four shell companies -- M/s Shalini Holdings Limited, M/s Ad- Fin Capital Services (India) Pvt. Ltd, M/s Mani Mala Delhi Properties Pvt. Ltd. And M/s Diamond Vinimay Pvt. Ltd.
These 1,20,000 shares, they said, were allegedly bought back by Bharti at Rs 10 per share.
The ED had also arrested Rajesh Agarwal, a chartered accountant allegedly linked to Bharti, who provided accommodation entries (black funds) of about Rs 60 lakh to M/s Mishail Printers and Packers Private Limited.
The searches, officials said, are part of investigations to unravel these links which allegedly routed black money using the shell companies in question.
Shell companies are firms set up with nominal paid up capital, high reserves and surplus on account of receipt of high share premium, investment in unlisted companies and no dividend income or high amount of cash-in-hand.
The ED is the third agency probing alleged financial irregularities by the Lalu Prasad family after the CBI and the Income Tax department which recently attached benami assets worth about Rs 180 crore (market value) in its investigation against them.
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