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Mathematics

Richard borrows ₹ 10,000 from his friend Ramesh. Ramesh asks him to return the money just by repaying ₹ 10 at first day and double the amount in the subsequent days than the each previous day continuously for 10 days. Richard thanks Ramesh for his help. Determine whether Ramesh was in loss or profit.

GP

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Answer

Sequence :

10 + 20 + 40 + ……… upto 10 terms.

The above is a G.P. with first term (a) = 10 and common ratio (r) = 2.

By formula,

Sn = a(rn−1)(r−1)\dfrac{a(r^n - 1)}{(r - 1)}

Substituting values we get :

⇒S10=10×(210−1)2−1=10×(1024−1)=10×1023=10,230.\Rightarrow S_{10} = \dfrac{10 \times (2^{10} - 1)}{2 - 1} \\[1em] = 10 \times (1024 - 1) \\[1em] = 10 \times 1023 \\[1em] = 10,230.

Since, Ramesh lent ₹ 10,000 but received ₹ 10,230 thus he is in profit of ₹ 230.

Hence, Ramesh makes a profit of ₹ 230.

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