A sum of ₹3200 was to be divided between A, B, C and D in the ratio 4: 6 : 7: 3. But by mistake, it was divided in the ratio 3 : 5 : 6 : 2. As a result, who got $$16\frac{2}{3}\%$$ less than her due?

A sum of ₹3200 was to be divided between A, B, C and D in the ratio 4: 6 : 7: 3.

Money got by A = $$3200\ of\ \left(\frac{4}{4+6+7+3}\right)$$ = $$3200\ of\ \left(\frac{4}{20}\right)$$ = 640

Money got by B = $$3200\ of\ \left(\frac{6}{4+6+7+3}\right)$$ = $$3200\ of\ \left(\frac{6}{20}\right)$$ =960

Money got by C = $$3200\ of\ \left(\frac{7}{4+6+7+3}\right)$$ = $$3200\ of\ \left(\frac{7}{20}\right)$$ = 1120

Money got by D = $$3200\ of\ \left(\frac{3}{4+6+7+3}\right)$$ = $$3200\ of\ \left(\frac{3}{20}\right)$$ = 480

But by mistake, it was divided in the ratio 3 : 5 : 6 : 2.

Money got by A = $$3200\ of\ \left(\frac{3}{3+5+6+2}\right)$$ = $$3200\ of\ \left(\frac{3}{16}\right)$$ = 600

Money got by B = $$3200\ of\ \left(\frac{5}{3+5+6+2}\right)$$ = $$3200\ of\ \left(\frac{5}{16}\right)$$ =1000

Money got by C = $$3200\ of\ \left(\frac{6}{3+5+6+2}\right)$$ = $$3200\ of\ \left(\frac{6}{16}\right)$$ = 1200

Money got by D = $$3200\ of\ \left(\frac{2}{3+5+6+2}\right)$$ = $$3200\ of\ \left(\frac{2}{16}\right)$$ = 400

Here only A and D got less than their initial. But only D got $$16\frac{2}{3}\%$$ less than from his initial.