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- 31. The compound interest on a sum for 2 years is Rs. 832 and the simple interest on the same sum for the same period is Rs. 800. The difference between the compound and simple interest for 3 years will be

A.Rs. 48

B.Rs. 98.56

C.Rs. 66.56

D.None of these

Answer & Explanation

Answer: Option B

Explanation:**Given that simple interest for 2 years is Rs.800**

i.e., Simple interest for 1st year is Rs.400

and simple interest for 2nd year is also Rs.400

Compound interest for 1st year will be 400

and Compound interest for 2nd year will be 832 - 400 = 432

you can see that compound interest for 2nd year is more than simple interest for 2nd year by 432 - 400 = Rs.32

i.e, Rs. 32 is the interest obtained for Rs.400 for 1 year

Rate, R = 100 × SI/PT = (100×32)/(400 × 1) = 8%

Difference between compound and simple interest for the 3rd year

= Simple Interest obtained for Rs.832

= PRT/100 = (832 × 8 × 1)/100 = Rs. 66.56

Total difference between the compound and simple interest for 3 years

= 32 + 66.56 = Rs.98.56

i.e., Simple interest for 1st year is Rs.400

and simple interest for 2nd year is also Rs.400

Compound interest for 1st year will be 400

and Compound interest for 2nd year will be 832 - 400 = 432

you can see that compound interest for 2nd year is more than simple interest for 2nd year by 432 - 400 = Rs.32

i.e, Rs. 32 is the interest obtained for Rs.400 for 1 year

Rate, R = 100 × SI/PT = (100×32)/(400 × 1) = 8%

Difference between compound and simple interest for the 3rd year

= Simple Interest obtained for Rs.832

= PRT/100 = (832 × 8 × 1)/100 = Rs. 66.56

Total difference between the compound and simple interest for 3 years

= 32 + 66.56 = Rs.98.56

- 32. A sum of money on compound interest amounts to Rs. 8240 in 2 years and Rs. 9888 in 3 years. The rate of interest is

A.10%

B.25%

C.20%

D.12%

Answer & Explanation

Answer: Option C

Explanation:**Let the sum be P and rate of interest be R% per annum.**

Amount after 2 year = 8240

P(1+R/100)T = 8240

P(1+R/100)2 = 8240 --- ( 1)

Amount after 3 year = 9888

P(1+R/100)T = 9888

P(1+R/100)3 = 9888 --- (2)

(2) ÷ (1) => [P(1 + R/100)3]/[P(1+R/100)2 = 9888/8240

1+R100 = 9888/8240

R/100 = (9888/8240 − 1 )= 1648/8240 = 15

R = 100/5 = 20%

Amount after 2 year = 8240

P(1+R/100)T = 8240

P(1+R/100)2 = 8240 --- ( 1)

Amount after 3 year = 9888

P(1+R/100)T = 9888

P(1+R/100)3 = 9888 --- (2)

(2) ÷ (1) => [P(1 + R/100)3]/[P(1+R/100)2 = 9888/8240

1+R100 = 9888/8240

R/100 = (9888/8240 − 1 )= 1648/8240 = 15

R = 100/5 = 20%

**Solution 2
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**If a certain sum of money at compound interest amounts to Rs.x in t1 years and Rs.y in t2 years, then the rate of interest per annum can be given by**

R = [(y/x)<sup>1/(t2−t1)</sup> − 1] × 100%

R = [(y/x)<sup>1/(t2−t1)</sup> − 1] × 100 = [(9888/8240)<sup>1/(3−2)</sup> − 1] × 100 = [(9888/8240) − 1] × 100

= (1648/8240) × 100 = (15) × 100 = 20%

R = [(y/x)<sup>1/(t2−t1)</sup> − 1] × 100%

R = [(y/x)<sup>1/(t2−t1)</sup> − 1] × 100 = [(9888/8240)<sup>1/(3−2)</sup> − 1] × 100 = [(9888/8240) − 1] × 100

= (1648/8240) × 100 = (15) × 100 = 20%

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