Prakash lends a part of ₹20,000 at 8% simple interest

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Prakash lends a part of ₹20,000 at 8% simple interest and remaining at 4 %
3

simple interest. His total income after a year was ₹800. Find the sum lent at 8%.

According to question ,
Let Amount lent at 8% rate of interest = ₹ p

∴ Amount lent at	4	% rate of interest = (20,000 – p)
	3

∴ SI =	Principal × Time × Rate
	100

∴	p × 8 × 1	+	(20000 - p) × ( 4/3 ) × 1	= 800
	100		100

⇒	2p	+	20000 - p	= 800
	25		75

⇒	6p + 20000 - p	= 800
	75

⇒ 5p + 20,000 = 75 × 800 = 60,000
⇒ 5p = 60,000-20,000 = 40,000
⇒ p = 40000 ÷ 5 = 8000