CPT CA MATH TRICKS AND CALCULATOR SHORTCUTS TO PASS/CRACK/CLEAR CPT MATH

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Jun 8, 2017
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MATH SHORTCUTS AND TRICKS:-

INTEREST AND ANNUITIES,

EQUATIONS,PROGRESSIONS

Q.200 for the first day of extra time required and thereafter forfeited amount is increased by Rs 25 for every day. If he loses 9,450, for how many days did he over-run the contract time? (a) 19 days (b) 21 days (c) 23 days (d) 25 days a = 200 d = 25 Sn = 9450 n = ? Sn = n [ 2a+(n-1)d] 2 9450 = n [2(200)+(n-1)25] 2 18900 = n[ 400 + 25n – 25] 18900 = 400n + 25n2 – 25n 18900 = 375n + 25n2 756 = 15 n + n2 15 n + n2 = 756 Try all options n = 19 n = 21 n = 23 n = 25 15 (19) + 192 = 646 15 (21) + 212 = 756 (b) Q. In an A.P. if the 3rd term is 18, 7 term is 30 then the sum of first 20 terms is: • (a) 810 (b) 520 (c) 180 (d) 250 • T3 = 18 T7 = 30 d = Difference between nth term Difference between n = 30 – 18 7 - 3 = 3 T3 = 18 a+2d = 18 a = 18 – 2d a = 18 – 2(3) a = 18 – 6 a = 12 Sn = n [ 2a+(n-1)d] 2 S20= 20 [2(12)+(20-1)3] 2 = 10 [ 24+ 57] = 810 (a) Q. Find compound interest on a sum of Rs.2500 invested for 4 years at 12% rate of interest compounded yearly •• (a) 1420 (b)1434 (c) 450 (d) None of these 2500 + 12% + 12% + 12% + 12% - 2500 1434 (b) Q. Effective rate of 6% of compounded half yearly •• (a) 6.06% (b) 6.09% (c) 6.08% (d) 6.07% 100 + 3% + 3% - 100 6.09 (b) 16 • The Partners A & B together lent Rs. 3903 at 4% p.a interest compounded annually. After a span of 7 years, A gets the same amount as B gets after 9 years. The share of A in the sum of Rs.3903/- would have been •• (a) Rs.1875 (b) Rs.2280 (c) Rs.2028 (d) Rs.2820 Trying all options a) b) c) d) A 1875 2280 2028 2820

B = 3903-A 2028 1623 1875 1083 A interest =A(1.04)7 2467 3000 2669 3711 B interest =A(1.04)9 2886 2310 2669 1541 (c) Q. The difference between CI and SI on a certain sum of money for 2 years at 4% per annum is Rs.1. The sum is •• (a) 625 (b) 630 (c) 640 (d) 635 Fci –Fsi = CI – SI P(1+0.04)2 – P(1+0.04*2) = 1 P[ 1.042 – 1.08] = 1 P[ 0.0016 ] = 1 P = 1/0.0016 P = 625 (a) Shortcut 1 / 4% / 4% = 625 applicable only for two years Q. The difference between and C.I & S.I at 7% p.a for 2 years is Rs. 29.4. then principal is •• (a) Rs.5,000 (b) Rs.5,500 (c) Rs.6,000 (d) Rs.6,500 29.4 / 7% / 7% = 6000 (c) Q. The present value of an annuity of Rs.1,000 made annually for 5 years at the rate of interest 14% compound annually is • (a) Rs.5610 (b) Rs.6610 (c) Rs.3433 (d) Rs.5160 • Present value of an annuity = A [(1+i)n - 1] i (1+i)n = 1000 [(1+0.14)5 - 1] 0.14 (1+0.14)5 = 7142.86 [ 1.145 – 1] 1.145 = 7142.86*(1.9254 – 1) 1.9254 = 3433 (c) Shortcut using GT 1/1+ i = = ..no of years A * GT = P Shortcut using GT 1/1.14 = = = = = 1000 * GT = 3433 Shortcut using MRC 1/1+ i =M+ =M+ ..no of years A * MRC = P Shortcut using MRC 1/1.14 = M+ = M+ = M+ = M+ = M 1000 * MRC = 3433 Q. The Future of an annuity of Rs.1,000 made annually for 5 years at the rate of interest 14% compound annually is • (a) Rs.5610 (b) Rs.6610 (c) Rs.3433 (d) Rs.5160 Future value of an annuity = A [(1+i)n - 1] i = 1000 [(1+0.14)5 - 1] 0.14 = 7142.86 [ 1.145 – 1] = 7142.86*(1.9254 – 1) = 6610 (b) Shortcut using GT 1/1+ i = = ..no of years A * GT = + i for number of years Shortcut using GT 1/1.14 = = = = = 1000 * GT = 3433+14%+14%+14%+14%+14% 6610 Shortcut using MRC 1/1+ i =M+ =M+ ..no of years A * MRC = P + I for number of years Shortcut using MRC 1/1.14 = M+ = M+ = M+ = M+ = M 1000 * MRC = 3433 + 14%+14%+14%+14%+14% 6610 Q. Find the the FV of annuity of 5000/- made annually for 8 years at Interest rate of 9% • (1.09)8 = 1.99256 •• (a) 55142.22 (b) 65142.22 (c) 65532.22 (d) 57425.2 1/1.09 = = = = = = = = GT * 5000 *1.99256 =55142 (a) Q. A man purchased a house valued at Rs. 300000. He paid Rs. 200000 at the time of purchase and agreed to pay the balance with interest at 12% per annum compounded half yearly in 20 equal half yearly instalments. If the first instalment is paid after six months from the date of purchase then the amount of each instalment is •• (a) Rs. 8719.66 (b) Rs. 8769.21 (c) Rs. 7893.13 (d) None of these Loan = 300,000,-200,000 = 100,000 P = 100,000 i = 12% p.a or 6% for half year n = 20 half years A = ? Using shortcut 1/1.06 = = = = = = = = = = = = = = = = = = = = 100000/GT = 8719 (a) Q. X limited is planning to purchase a machinery costing Rs 50000 with useful life of 5 years . Company has two options Option A : Borrow Rs.50000 at interest rate of 10% and buy machinery and repay in 5 years Option B : Obtain the same on lease for 5 years with Rs 12000 per annum as lease rental • The company should opt for • (a) Borrowing (b) Leasing (c) Can’t say (d) Either borrow or lease Option A Borrow today 50,000 Option B Lease 12000 p.a for 5 years Equivalent borrowing today = PV of annuity 1/1.1 = = = = = GT * 12000 45489 Leasing is cheaper (b) Q. If x+5y=33 and (x+y)/(x-y) = 13/3 then x and y is •• (a) (4,8) (b) (8,5) (c) (4,6) (d) (16,4) • x+5y=33 • Substitute by all options • (a) x = 4, y = 8 4 + 5(8) = 33 4 + 40 ≠ 33, LHS ≠ RHS • (b) x = 8, y = 5 8 + 5(5) = 33 33 = 33, LHS = RHS • (c) x = 4, y = 6 4 + 5(6) = 33 4 + 30 ≠ 33, LHS ≠ RHS • (d) x = 16, y = 4 16 + 5(4) = 33 16 + 20 ≠ 33, LHS ≠ RHS (b)

Q. A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. What is the basic first class full fare and what is the reservation charge? •• (a) Rs. 105 and Rs. 6 (b) Rs.216 and Rs. 12 (c) Rs. 210 and Rs. 12 (d)Rs. 210 and Rs. 6 • One reserved ticket costs Rs. 216 • Try all options • 105 + 6 ≠ 216 • 216 + 12 ≠216 • 210+12 ≠216 • 210 + 6 = 216 • (d) Q. A number consisting of two digits is four times the sum of its digits and if 27 be added to it the digits are reversed. The number is •• (a) 63 (b) 35 (c) 36 (d) 60 • 27 added numbers reversed • Try all options • 63 + 27 = 90 • 35 + 27 = 62 • 36 + 27 = 63 • 60 + 27 = 87 • (c)

Q. Mrs. B. invested Rs.30,000; part at 5%, and part at 8%. The total interest on the investment was Rs.2,100. How much did she invest at each rate? •• (a) Rs 10000, 20000 (b) Rs 15,000, 20,000 (c) Rs 15000, 25000 (d) Rs 10,000, 30,000 • Investment 30,000 • Try all options • 10,000+20,000 =30,000 • 15000 + 20000 ≠ 30000 • 15000+ 25000 ≠ 30000 • 10000 + 30000 ≠ 30000 • (a) Q. 3x–4y+70z = 0, 2x+3y–10z = 0, x+2y+3z = 13 •• (a) (1, 3, 7) (b) (1, 7, 3) (c) (2, 4, 3) (d) (–10, 10, 1) •• 3x–4y+70z = 0 • Try all options • 3(1)–4(3)+70(7) = 481≠ 0 • 3(1)–4(7)+70(3) = 185≠ 0 • 3(2)–4(4)+70(3) =200 ≠ 0 • 3(-10)–4(10)+70(1) = 0 • (d) Q. One root of x2 – 3x+ k = 0 is 2 then k is •• (a) -10 (b) 0 (c) 2 (d) 10 • x2 – 3x+ k = 0 • X = 2 • 22 – 3(2)+ k = 0 • 4 – 6 + k = 0 • K = 2 • (c)