R' invested some money at a compound interest rate of 40% p.a., compounded quarterly. If after 9 months, he received an amount of Rs. 1,99,650, then the sum invested by 'R' is equal to:
I. The interest received when Rs. 1,25,000 is invested at S.I of 30% p.a. for 4 years.
II. The
C.P of an item sold for Rs. 2,40,000 at a profit of 40%.
III. The difference between the savings of 'Pawan' and 'Qureshi', whose incomes are Rs. (a + 406320) and Rs. (a + 156320), given that each spends 40% of their respective incomes.

ATQ, Effective rate of interest = 40 ÷ 4 = 10% p.a. And effective time period = (9/12) × 4 = 3 terms We know that for compound interest, Amount = Sum × {1 + (rate of interest/100)} time period Let the sum invested be Rs. 'S' So, 199650 = S X {1 + (10/100)} ³ Or, 199650 = S X (1.1) ³ Or, 199650 = 1.331S So, S = 1,50,000 Therefore, sum invested = Rs. 1,50,000 For I: Interest received = (125000 × 0.3 × 4) = Rs. 1,50,000 Therefore, statement I is true. For II: CP of the item = (240000/1.4) = Rs. 171428.57 Therefore, statement II is false. For III: Difference between savings of 'Pawan' and 'Qureshi' = 0.6 × (a + 406320) - 0.6 × (a + 156320) = 0.6 × (406320 - 156320) = 0.6 × 250000 = Rs. 1,50,000 Therefore, statement III is true.