Question
X invested M in scheme a that offers __% rate of simple
interest and M - 1000 in scheme b that offers __% rate of simple interest. X gets total interest of Rs.4620 from both schemes after two years and if X invests the whole amount in scheme c at the rate of 20% simple interest for 4 years, then the interest earned is Rs.5000. Which of the following can fill in the blanks? I) 18 and 36 II) 25 and 44 III) 42 and 30 IV) 12 and 45Solution
ATQ, If X invested in scheme C, then principal would be (P) P = interest received / (rate × time) P = 5000 / (20% × 4) P = 5000 / 0.8 P = 6250 Now, M + (M - 1000) = 6250 2M - 1000 = 6250 2M = 7250 M = 3625 So, Investment in scheme a = 3625 Investment in scheme b = 2625 Now check the options: From I, Total interest = 3625 × 18 × 2/100 + 2625 × 36 × 2/100 = 1305 + 1890 = 3195 Not equal to 4620 From II, Total interest = 3625 × 25 × 2/100 + 2625 × 44 × 2/100 = 1812.5 + 2310 = 4122.5 Not equal to 4620 From III, Total interest = 3625 × 42 × 2/100 + 2625 × 30 × 2/100 = 3045 + 1575 = 4620 This matches From IV, Total interest = 3625 × 12 × 2/100 + 2625 × 45 × 2/100 = 870 + 2362.5 = 3232.5 Not equal to 4620 Hence, only III fits.
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