4 Mark Question

Question 14 Marks

Find the time when:
A sum when reckoned at $7\frac12\%$ per annum amounts to Rs. 3920 in 3 years. Find the sum.

Answer

Let the required sun be Rs. xA = Rs. 3920,
$\text{R}=7\frac12\%,$
T = 3 years
Now, $\text{S.I.}=\frac{\text{P}\times\text{r}\times\text{t}}{100}$
$=\frac{\text{x}\times15\times3}{2\times100}$
$=\frac{9\text{x}}{40}$
$\text{A}=\text{P}+\text{S.I.}$
$=\text{x}+\frac{9\text{x}}{40}$
$=\frac{40\text{x}+\text{9x}}{40}$
$=\frac{49\text{x}}{40}$
But the Amount is Rs. 3920
$\Rightarrow\frac{49\text{x}}{40}=3920$
$\Rightarrow\text{x}=\frac{3920\times40}{49}$
$\Rightarrow\frac{156800}{49}=3200$
Hence, the required sum is Rs. 3200

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Question 24 Marks

Find the time when:
A sum of money lent at simple interest amounts to Rs. 783 in 2 years and to Rs. 837 in 3 years. Find the sum and the rate per cent per annum.

Answer

Amount in 3 years = (Principal + S.I. for 3 years) = Rs. 837
Amount in 2 years = (Principal + S.I. for 2 years) = Rs. 783
On subtracting:
S.I. for 1 years = (837 - 783) = Rs. 54
$\text{S.I. for 2 years}=\Big(\frac{54}{1}\times2\Big)=\text{Rs. }108$
$\therefore$ Sum = Amount for 2 years - S.I. for 2 years
$=783-108$
$=\text{Rs. 675}$
P = Rs. 675, S.I. = Rs. 108 and T = 2 years
$\text{r}=\frac{\text{S.I.}\times100}{\text{P}\times\text{t}}$
$=\frac{108\times100}{675\times2}$
$=8\%$

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Question 34 Marks

Find the time when:
A sum of money becomes $\frac85$ of itself in 5 years at a certain rate of simple interest. Find the rate of interest.

Answer

Let the sum be Rs. x$\text{Amount}=\frac{8\text{x}}{5}$
$\therefore\text{S.I.}=\text{A}-\text{P}=\frac{\text{8x}}{\text{5}}-\text{x}$
$=\frac{3\text{x}}{5}$
Let the rate be r%
$\text{S.I.}=\frac{\text{P}\times\text{r}\times\text{t}}{100}$
$\Rightarrow\frac{3\text{x}}{5}=\frac{\text{x}\times\text{r}\times5}{100}$
$\Rightarrow\text{3x}\times20$
$\Rightarrow\text{r}\times\text{x}\times5$
$\Rightarrow\text{r}=\frac{3\times\text{x}\times20}{\text{x}\times5}=12$
Hence, the rate of interest is 12%.

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Question 44 Marks

Find the time when:
If Rs. 640 amounts to Rs. 768 in 2 years 6 months. What will Rs. 850 amount to in 3 years at the same rate per cent per annum?

Answer

In first case,
Amount (A) = Rs. 768
Principal (P) = Rs. 640
S.I. = A - P = Rs. 768 - 640
= Rs. 128
$\text{Time(t)}=2\text{ years}\ 6\text{ months}=2\frac12$
$=\frac52\text{ years}$
$\therefore\text{Rate}=\frac{\text{S.I.}\times100}{\text{P}\times\text{r}}$
$=\frac{128\times100\times2}{640\times5}$
$=8\%\text{ p.a.}$
In second case,
Principal (P) = Rs. 850
Rate (r) = 8% p.a.
Time (t) = 3 years
$\therefore\text{S.I.}=\frac{\text{P}\times\text{r}\times\text{t}}{100}$
$=\frac{850\times8\times3}{100}$
$=\text{Rs. }204$
$\text{Amount}=\text{P}+\text{S.I.}$
$=\text{Rs. }850+\text{Rs. }204$
$=\text{Rs. }1054$

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Maths 4 Mark Question

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