1. B Solution: On SI, Rate for 3 years=3*10=30% On CI rate for 3 years – 10%=1/10 10—–11 10—–11 10—–11 1000—-1331 =1331-1000/1000 *100=33.1% Difference=33.1-30=3.1% 3.1%=930 100%=Rs 30,000

2. C Solution: a————————b—————c 5000—————– X ————16200 ———–t——————- t ———— As we have to calculate the sum for half time, both time period is same, and hence a:b = b:c 5000:x = x:16200 x=Rs 9000

3. A Solution: In C.I P increases like P——-2P——–4P———8P——–16P

—-3yrs—–3yrs—–3yrs——-3yrs total=3+3+3+3=12 years

4. D Solution: At 10% CI in 2 years=21 % At 20% Ci in 2 years =44% and 5350 is 107/4% of 20000, by using allegation A B 21 44 107/4 3 1 A=3/4*20000= Rs 15000

5. B Solution: SI for 2 years = Rs 1000 =.> Si 1 year = Rs 500 In the second years Rs 25 is added in CI (1025-1000) which is 5% of 500 Hence R=5% 5%=500 100%=10000 sum=10000 CI for 3 years= RS 1576.25

6. C Solution: SI=A-P=> A=3P as sum triples SI=3P-P=2P in 6 years In 19 times SI=18 P—54 years (2:6 hence 18=54)

7. A Solution: Sum=353; Amount=512

as many year, put that many root i.e cuberoot(343): cuberoot(512) 7:8 rate=(8-7)/7 *100 =14 (2/7)%

8. B Solution: In half yearly=> Time-double; Rate= half Rate=5% ; Time=4 years; Sum = Rs 20,000 1 years————–2 years————3 years———-4 years 1000—————–1000—————1000————-1000 ————————50——————50—————–50 ———————————————50—————–50 ———————————————2.5—————-50 —————————————————————–2.5 —————————————————————–2.5 —————————————————————–2.5 —————————————————————-0.125 Total = Rs 4000 +300 + 10+0.125= Rs 4310.125

9. C Solution: Formula= x/(1+R/100)^T x/ (1+20/100)^1 + x/(1+20/100)^2 = 6600 solve and get x=4320

10. B Solution: Sum= A Interest= B A——–A———A ———-B———B

———————B ———————C CI for 3 years=3A+3B+C SI for 3 years =3A Diff= 3B+cCI for 2 years=2A+B SI for 2 years=2A diff=B ratio=(3B+C)/B=31/10 B=10; C=1 Rate=C/B=1/10=10%

11. C Explanation: S.I.=1000∗10∗4/100=400C.I.=[1000(1+10/100)4−1000]=464.10S.I.=1000∗10∗4100=400C.I.=[1000(1+10/100)4−1000]=464.10 So difference between simple interest and compound interest will be 464.10 - 400 = 64.10

12. C Please remember, when we have to calculate C.I. quarterly then we apply following formula if n is the number of years Amount=P(1+R/4/100)4n Principal = Rs.16,000; Time=9 months = 3 quarters; Rate = 20%, it will be 20/4 = 5%

So lets solve this question now, Amount=16000(1+5100)3=18522C.I=18522−16000=2522

13. B Explanation: Amount=[7500×(1+4/100)2]=(7500×26/25×26/25)=8112Amount=[7500×(1+4/100)2]=(7500×26/25×26/25)=8112 So compound interest = (8112 - 7500) = 612

14. B Explanation: Let the Sum be P S.I.=P∗4∗2/100=2P/25 C.I.=P(1+4/100)2−P=676P/625−P=51P/625As, C.I. - S.I = 1=> 51P/625−2P/25=1 =>51P−50P/625=1 P=625

15. B In this type of question we apply formula Amount=P/(1+R/100)n Amount=169/(1+4/100)2 Amount=169∗25∗25/26∗26 Amount=156.25

16. B C.I.=(4000×(1+10/100)2−4000)=4000∗11/10∗11/10−4000=840 So S.I. = 8402=420 So Sum = S.I.∗100/R∗T= 420∗100/3∗8 =Rs1750

17. B Explanation: Principal = Rs.1000; Amount = Rs.1331;

Rate = Rs.10%p.a. Let the time be n years then,

1000(1+10/100)n=1331 (11/10)n=1331/1000 (11/10)3=1331/1000

So answer is 3 years 18.C Explanation : P*(1+5/100)^4 – P – P*(10/100)*2 = 248.10 P = 16000 19. A Explanation : 240 = P*(5/100)*2, P = 2400 CI = 2400(1+5/100)^2 – 2400 = 246 So, 246 – 240 = 6 20. C Explanation : Amount >= P*(1+25/100)^n Amount = p*(5/4) ^n For n = 4, (625/256) which is greater than 2. 21. B Explanation : Let the share of rakesh and prakash be R and P R*(1+10/100)^ 5 = (4420 – R)*(1+10/100)^ 7 We get R = 2420, so P = 2000 22. C

Explanation : 600 = p*4*(15/100), P = 1000 CI = 1000(1+10/100)^ 2 – 1000 = 210 23. B Explanation : Take principal as 100 and then calculate, A = 100*(1+5/100)^ 2 A = 110.25 So effective rate is 10.25 24. C Explanation : Rate of interest is 25 paise per rupee per annum. So for 100 rupees it is 2500 paise i.e. 25 percent Now, CI = 3200(1+25/100)^ 2 – 3200 = 1800 25. B Explanation : 3600 = 3000*(1+15/100)^ 3 (1+15/100)^ 3 = 6/5 Amount = 3000*[(1+15/100)^ 3]^ 3 Amount = 3000*(6/5)^ 3 = 5184 26. A Explanation : Total amount = 500*(1+10/100)^ 3 + 500*(1+10/100)^ 2 + 500*(1+10/100) = 1820.5 27. D Explanation : Amount to be paid at the end of three years = 10000*(1+20/100)^ 3 = 17280 Amount paid as instalment by the man = 2000*(1+20/100)^

2 + 2000*(1+20/100) + 2000 = 7280 So remaining amount = 10000 28. C Explanation : 10*3*x/5*2*y = 1/2 x/y = 1/6 6/7*70000 = 60000 29. D Explanation : In S.I, Let P=100, I=50, T=5 yrs R = 50*100/100*5 = 10% In C.I, P = 12000, T=3 yrs, R= 10% C.I = [12000*(1 + 10/100)^3 – 1 ] C.I = 3972. 30. C Explanation : SI=20*2=40% CI=20+20+(400/100)=44% Diff = 44-40=4% 31. C Explanation : After one year amount = 3000 *110/100 = 3300 He pays 1000 back, so remaining = 3300-1000 = 2300 After two year amount = 2300 *110/100 = 2530 He pays 1000 back, so remaining = 2530-1000 = 1530 After three year amount = 1530*110/100 = 1683 He pays 1000 back, so remaining = 1683-1000= 683 After fouth year = 683 * 110/100 = 751.3 32. D

Explanation : 800*(11/10)³=1064.8 800*(11/10)²=968 800*(11/10)=880 Total amount =2912.8 33. C Explanation : SI =300 Per yr = 100 Rate = 10% C.I = 1000*(108/100)³ -1000 C.I = 259.712 34. D Explanation : Difference = Pr2/(100)2 = (450×100×100)/(P×r2) P is not given 35. D Explanation : A = 6000*108/100*107/100*106/100 = 6000*1.08*1.07*1.06 = 7349.616 = 7350 CI = 7350-6000 = 1350 36. B Explanation : D =[(30,000 *110/100*110/100) – 30,000] – 30,000 *10*2/100 =[36300-30000]- 6000 =6300 – 6000 D = 300

37. C Explanation : 4500*3/100(R1-R2) = 405 R1-R2 = 405*100/13500 = 3% 38. D Let the amount invested in scheme B is ₹ x. ∴ Amount invested in scheme A be ₹ (23000 – x). According to the question,

(23000 – x) + (23000 – x) × 20 × 1

= x + x ( 1 + 10

) 1 – x

100 100

⇒ (23000 – x) × 6

= 11x

5 10 ⇒ 11x = 276000 – 12x ⇒ 23x = 276000 ⇒ x = 12000 Hence, option D is correct. 39. C Let the amount taken from Suresh is x and amount taken from Raj =

18x 25

Amount taken from Akash = 32500 – x – 18x

= 32500 – 43x

25 25

Total interest he gives -

( 18x

) × 12

( 32500 – 43x

) × 16

⇒ 25

+ 25

+ x × 18

= 5090 (Given) 100 100 100

216x – 688x + 450x = 12725000 – 13000000 22x = 275000 x = 12500 Amount taken from Akash

= 32500 – 43 × 12500

= 32500 – 21500 = Rs.11000 25

Hence, option (C) is correct. 40. A Bede has Rs 90000 with him after paying 25% as gift tax.

Amount Invested

Interest Tax

Year 1

90000 9000 1800

Year 2

97200 9720 1944

Year 3

104976 10497.60 2099.52

Year 113374.08 11337.408 2267.4816

4 So, Bede has Rs. (113374.08 + 11337.408 – 2267.4816) = Rs. 122444 at the end of 4th year. Hence, option (A) is correct. 41. A Suppose the person has deposited Rs. X at the time of opening account. After one year, he had

Rs. ( x + x × 10 × 1

) = Rs. 11x

100 10 After two years, he had

Rs. ( 11x

+ 11x

× 10 × 1

) = 121x

10 10 100 100

After withdrawing Rs 5000 from Rs. 121x

, the balance 100

= Rs. 121x – 500000

100 After 3 years, he had 121x – 500000

+ 121x – 500000

× 10 × 1

100 100 100 = 11(121x – 500000)

1000 After withdrawing 6000 from above, the balance

= Rs. ( 1331x

– 11500 ) 1000

After 4 years, he had

Rs. 11

( 1331x

– 11500 ) – 10000 = 0 10 1000

⇒ Rs 15470 Hence, option (A) is correct. 42. D Let x = equal instalment at the end of each year Now 1st year, P = Rs. 1100

Interest at the end of 1st year = 1100 × 20 × 1

= Rs. 220 100

Now, at the beginning of 2nd year, P = Rs. (1100 + 220 – x) = Rs. (1320 – x) Interest at the end of 2nd year

= (1320 – x) × 20 × 1

= 264 – x

100 5

Now amount remaining after 2 years

= (1320 – x) + ( 264 – x

) – x = 0 5

⇒ 2x + x

= 1320 + 264 5

⇒ 11x

= 1584 5

⇒ X = 720 Hence, option (D) is correct. 43. A We know that

Rate = SI × 100

Principal × Time

= 7770 × 100

= 14% per annum 18500 × 3

We know the formula for compound interest -

⇒ CI = [ P { ( 1 + r

) t – 1 } ]

100 Where, CI = Compound interest

P = Principal R = Rate of interest T = Time period

= 18500 [ ( 1 + 14

) 3 – 1 ] = 18500 [(1.14)3 –1]

100 ⇒ 18500 × 0.481544 = Rs 8908.56 Hence, option (A) is correct. 44. D CI for 2 years 6 months at the rate of 6, applying the net% effect for first 2 years

= 6 + 6 + 6 × 6

= 12.36% 100

Rate of interest for 6 months = 6

× 6 = 3% 12

For next 6 months = 12.36 + 3 +

12.36 × 3

= 15.36 + 0.37% = 15.73%

100 Here, we can see that in 2 years 6 months the given compound rate of interest is approximate 15.73%.

Now, 115.73% of 250000 = 115.73 × 250000

= 289,325. 100

Hence, option D is correct. 45. E Approach I: To solve this question, we can apply the net % effect formula

x + y + xy

% 100

Compounded annually at rate 20% per annum for 2 years, we get

= 20 + 20 + 20 × 20

= 44% 100

Similarly, compounded half yearly at rate 10%, we get

= 10 + 10 + 10 × 10

= 21% 100

And, 21 + 10 + 21 × 10

= 33.1% 100

And, 33.1 + 10 + 33.1 × 10

= 46.41% 100

Now as per the question, Difference between compound interest yearly and half yearly = 46.41 – 44 = 2.41%

Given, 2.41% ≡ 482 100% ≡ x

⇒ x = 482 × 100

= 20,000 2.41

Approach II: When compounded annually, the amount received at the end of the period is

A = P [ 1 + r

] n

100 When compounded half yearly, the amount received at the end of the period is

A = P [ 1 + r/2

] 2n

100 Let the principle be P. Interest on this amount when compounded annually at the rate of 20% per annum = P [(1.20)2 − 1] Interest on this amount when compounded half yearly = P [(1.10)4 − 1] The difference between the two is Rs. 482 ∴ P [(1.10)4 − 1] – P [(1.20)2 −1] = 482 ∴ P [1.4641 – 1.44] = 482

∴ P = Rs. 20,000 Hence, option E is correct 46. D Total Income = 67,280 After giving 50% salary to his wife the man is left with an amount = 33,640 Let's assume the man gave Rs. x to A. Therefore B will get Rs. (33640 – x).

↙ 33640

↘

14 years A

12 years B x (33640 – x)

Now, as per the question A & B will be getting an equal amount with CI at 5% rate per year at the 18th year.

⇒ x ( 1 + 5

) 4

= (33640 – x) [ 1+ 5

] 6

100 100

⇒ x

(33640 – x)

= ( 1 +

5 )

6 100

( 1 +

5 )

4 100

⇒ x = ( 21 × 21 )

(33640 – x) 20 20 ⇒ 400 x = 33640 × 441 – 441x ⇒ 841x = 33640 × 441

x = 33640 × 441

= 40 × 441 = 17640/- 841

Therefore, at the time of divison of money, B would have got a sum = (33640 – 17640) = Rs. 16000 Hence, option D is correct. 47. C Lets first calculate the total rate % that Aditya will have after 3 years: As per the question Aditya invested at rate of 12% pa simple interst So, for 3 years tenure he will get = 12 × 3 = 36% And the amount that Bhushan invested at rate of 10% pa compound interest By net% effect formula, we can calculate the total perecntage for 3 years tenure = 33.1% (sub details) So, the difference between SI and CI = 36% – 33.1% = 2.9% (SI is more)

Here Aditya will get, 2.9% of 10000 = 290 So Aditya will have Rs. 290 more than Bhushan. --------------------------------------------------------------------------------- Sub-details:-

Net% effect = x + y = xy

% 100

For the first 2 years: Here, x = y = 10%

= 10 + 10 = 10 × 10

= 21% 100

And for the next year: Here x = 21% and y = 10%

= 21 + 10 = 21 × 10

= 33.1% 100

Hence, option C is correct. 48. B Let the each instalment be x.

x +

x = 9960

( 1 + 15

) ( 1 + 15

) 2

2 × 100 2 × 100

x + x = 9960

( 1 + 3

) ( 1 + 3

) 2

40 40

⇒ 40 x

+ 1600 x

= 9960 43 1849

⇒ 1720 x + 1600 x

= 9960 1849

⇒ 3320 x = 9960 × 1849 ⇒ x = Rs. 5547 Hence, option B is correct. 49. A Let the amount invested in scheme A is 2 × 50 = 100, the amount invested in scheme B is 5 × 50 = 250

Interest from scheme A = 100 × ( 1 + 30

) 2

100 = 169 – 100 = Rs.69 Interest from scheme B = 250 × 15% × 2 = Rs.75 Difference between interest = 75 – 69 = Rs.6 If the difference is Rs.6., investment in scheme B = Rs.250

so the difference is Rs.1080 .,

investment in scheme B =Rs. 250

× 1080. = Rs.45000 6

Hence, option A is correct. 50. B According to the question,

A ( 1 + 12

) 2 – A = (A + 1500) × 8% × 3

100

A × 112

× 112

– A = A × 24

+ 360 100 100 100

A × 12544

– A – A × 24

= 360 10000 100

12544A – 10000A – 2400A

= 360 10000

144A = 3600000 A = 25000 Amount invested by Reet = Rs 25000 Hence, option B is correct. 51. A

Explanation: For 1st year S.I =C.I. Thus, Rs.16 is the S.I. on S.I. for 1 year, which at 8% is thus Rs.200 i.e S.I on the principal for 1 year is Rs.200 Principle = Rs.100*2008*1Rs.100*2008*1 = Rs.2500 Amount for 2 years, compounded half-yearly Rs.[2500*(1+4100)4]=Rs.2924.4Rs.2500*1+41004=Rs.2924.4 C.I = Rs.424.64 Also, S.I=Rs.(2500*8*2100)=Rs.400S.I=Rs.2500*8*2100=Rs.400 Hence, [(C.I) - (S.I)] = Rs. (424.64 - 400) = Rs.24.64 52. B Explanation: Compound Interest on P at 10% for 2 years when interest is compounded half-yearly =P(1+R2100/)2T−P=P(1+120)4−P=P(2120)4−PP1+R21002T-P=P1+1204-P=P21204-P Simple Interest on P at 10% for 2 years = PRT100=P×10×2100=P5PRT100=P×10×2100=P5 Given that difference between compound interest and simple interest = 124.05 P*(2120)4−P−P5=124.05P*21204-P-P5=124.05

=>P[(2120)4−1−15]=124.05P21204-1-15=124.05 P=8000 53. B Explanation: Explanation:Let rate = R% and time = R years. Then, (1200*R*R100)=4321200*R*R100=432 12R2=43212R2=432 =>R2=36⇔R=6 54. B Explanation: difference in C.I and S.I in 2years =Rs.32 S.I for 1year =Rs.400 S.I for Rs.400 for one year =Rs.32 rate=[100*32)/(400*1)%=8% difference between in C.I and S.I for 3rd year =S.I on Rs.832= Rs.(832*8*1)/100=Rs.66.56 55. B Explanation: Difference in C.I and S.I for 2 years = Rs(696.30-660) =Rs. 36.30. S.I for one years = Rs330. S.I on Rs.330 for 1 year =Rs. 36.30 Rate = (100x36.30/330x1)% = 11% 56.B

Explanation: The population grew from 3600 to 4800 in 3 years. That is a growth of 1200 on 3600 during three year span. Therefore, the rate of growth for three years has been constant. The rate of growth during the next three years will also be the same. Therefore, the population will grow from 4800 by 4800*134800*13= 1600 Hence, the population three years from now will be 4800 + 1600 = 6400 57. A 5% is the rate of interest. 20% of the interest amount is paid as tax. i.e 80% of the interest amount stays back.

if we compute the rate of interest as 80% of 5% = 4% p.a., we will get the same value. The interest accrued for 3 years in compound interest = 3 x simple interest on principal + 3 x interest on simple interest + 1 x interest on interest on interest. = 3 x (200) + 3 x (8) + 1 x 0.32 =600 + 24 + 0.32 = 624.32 The amount at the end of 3 years = 5000 + 624.32 = 5624.32 58. B Explanation: Let the sum be Rs. P. Then,[p(1+10/100)2-p]=525 Sum =Rs.2500 S.I.= Rs.(2500*5*4)/100= Rs. 500 59. C

Explanation: Shyam's share * (1+0.05)9 = Ram's share * (1 + 0.05)11 Shyam's share / Ram's share = (1 + 0.05)11 / (1+ 0.05)9 = (1+ 0.05)2 = 441/400 Therefore Shyam's share = (441/841) * 5887 = 3087 60. A Explanation: Let the two parts be Rs. x and Rs. (1301 - x). x(1+4100)7=(1301−x)(1+4100)9x1+41007=1301-x1+41009 x(1301−x)=(1+4100)2=(2625*2526)x1301-x=1+41002=2625*2526 => 625x=676(1301-x) 1301x=676 x 1301x=676. So,the parts are rs.676 and rs.(1301-676)i.e rs.676 and rs.625 61. C Explanation: C.I.= Rs.[4000*(1+10/100)^2-4000] =Rs.840 sum=Rs.(420 * 100)/3*8=Rs.1750 62. C Explanation: The mathematical formula for calculating compound interest depends on several factors. These factors include the amount of money deposited called the principal, the annual interest rate (in decimal form), the number of times the money is compounded per year, and the number of years the money is left in the bank. FV=p(1+rn)ntFV=p1+rnnt

FV = Future value of the Deposit p = Principal or Amount of Money deposited r = Annual Interest Rate (in decimal form ) n = No of times compounded per year t = time in years FV=4000[1+0.064]4(5)FV=40001+0.0644(5)= 5387.42 63. D Explanation: Shawn received an extra amount of (Rs.605 – Rs.550) Rs.55 on his compound interest paying bond as the interest that he received in the first year also earned interest in the second year. The extra interest earned on the compound interest bond = Rs.55 The interest for the first year =550/2 = Rs.275 Therefore, the rate of interest =55275*10055275*100= 20% p.a. 20% interest means that Shawn received 20% of the amount he invested in the bonds as interest. If 20% of his investment in one of the bonds = Rs.275, then his total investment in each of the bonds =27520*10027520*100 = 1375. As he invested equal sums in both the bonds, his total savings before investing = 2 x 1375 =Rs.2750. 64. A 65. A Explanation: FV �= $1000(1.04)(1.045)(1.05)(1.055)(1.06) =� $1276.14 the maturity value of the regular GIC is FV =� $ 1000 x (1.05)51.055= � $1276.28

66. A Explanation: Given compound interest for 3 years = Rs. 1513.2 and simple interest for 5 years = Rs. 2400 Now, we know that C.I = [P(1+R100)n − 1]P1+R100n - 1 => 1513.2 = [P(1+R100)3 − 1]P1+R1003 - 1 ...........(A) And S.I = PTR/100 => 2400 = P5R/100 ..................(B) By solving (A) & (B), we get R = 5%. 67. C Explanation: Diff = 960-800 = 160 r = 2*Diff*100/SI So r = 2*160*100/800 = 40% Now 160 = Pr2/1002 68. D Explanation: 6000[1 + r/100]3 = 7200 So [1 + r/100]3 = 6/5 So 6000[1 + r/100]9 = 6000*(6/5)*(6/5)*(6/5) 69. E Explanation: Amount after 1 yr = 4000[1 + 8/100] = 4320 Paid 500, so P = 4320 – 500 = 3820 Amount after 2nd yr = 3820[1 + 8/100] = 4125.6 So P= 4125.6-500 = 3625.6 Amount after 3rd yr = 3625.6[1 + 8/100] = 3915.6 70. B

Explanation: P[1 + (r/2)/100]4 – P[1 + r/100]2 = 482 P[1 + 10/100]4 – P[1 + 20/100]2 = 482 Solve, P = 20,000 71. B Explanation: Difference in interest for both yrs = 172.8 – 160 = 12.8 So (r/100)*160 = 12.8 72. A Explanation: P[1 + r/100]3 = 37,044, and P[1 + r/100]2 = 35,280 Divide both equations, [1 + r/100] = 37044/35280 = 21/20 So P[21/20]2 = 35280 73. A Explanation: [P[1 + 5/100]3 – P] – P*4*4/100 = 76 P [9261/8000 – 1 – 16/100] = 76 74. C Explanation: Difference in 3 yrs = Pr2(300+r)/1003 Difference in 2 yrs = Pr2/1002 So Pr2(300+r)/1003 / Pr2/1002 = 35/11 (300+r)/100 = 35/11 75. D Explanation: P = 882/[1 + 5/100] + 882/[1 + 5/100]2 76. B Explanation: A’s share = (1 + 4/100)7 B’s share = (1 + 4/100)9

Divide both, B/A = (1 + 4/100)2 = 676/625 So A’s share = 625/(676+625) * 3903 77.B Explanation: Let the sum be Rs. P P{ (1+8100)2- 1 } = 2828.80 It is in the form of a2-b2 = (a+b)(a-b) P(8/100)(2 + 8/100) = 2828.80 P = 2828.80 / (0.08)(2.08) = 1360/0.08 = 17000 Principal + Interest = Rs. 19828.80 78. C Explanation: C.I. =Rs[4000x(1+10/100)²-4000] Rs.(4000x11/10x11/10-4000) = Rs.940. Sum =Rs. [420 *100 /3 * 8]= Rs.1750. 79. A Explanation: Let the sum be Rs.x. Then, [x(1+10100)2-x]=1155 ⇒x[(1110)2-1]=1155 => x =5500 sum = Rs. 5500. So, S.I = Rs. (5500×5×4100) = 1100 80. B Let the sum(principal) received by A and B are x and y. (1+r) = =

Then, = Hence, the ratio in which the sum is divided =121:100

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