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Mathematics

Mohan lends ₹ 4,800 to John for 4124\dfrac{1}{2} years and ₹ 2,500 to Shyam for 6 years and receives a total sum of ₹ 2,196 as interest. Find the rate per cent per annum, provided it is the same in both the cases.

Simple Interest

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Answer

For Mohan,

P = ₹ 4,800

T = 4124\dfrac{1}{2} years

= 92\dfrac{9}{2} years

Let the rate be rr

S.I.=(P×R×T100)=(4,800×r×92×100)=(43,200r200)=216r\text{S.I.} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = \Big(\dfrac{4,800 \times r \times 9}{2 \times 100}\Big)\\[1em] = \Big(\dfrac{43,200r}{200}\Big)\\[1em] = 216r

For Shyam,

P = ₹ 2,500

T = 6 years

Let the rate be rr

S.I.=(P×R×T100)=(2,500×r×6100)=(15,000r100)=150r\text{S.I.} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = \Big(\dfrac{2,500 \times r \times 6}{100}\Big)\\[1em] = \Big(\dfrac{15,000r}{100}\Big)\\[1em] = 150r

Total interest = ₹ 2,196

₹ 216r + ₹ 150r = ₹ 2,196

₹ 366r = ₹ 2,196

r = 2196366\dfrac{2196}{366}

r = 6%6\%

Hence, the rate per cent per annum = 6%.

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