Interest - Aptitude MCQ Questions and Solutions with Explanations

Let the money added by Rahul be Rs. x
Then,
$$ \Rightarrow \frac{{\left( {1150 + x} \right) \times 9 \times 3}}{{100}} - $$     $$\frac{{1150 \times 6 \times 3}}{{100}} = $$    $$274.95$$
⇒ 1150 × 27 + 27x - 1150 × 18 = 27495
⇒ 27x + 1150 × (27 - 18) = 27495
⇒ 27x = 27495 - 10350
⇒ 27x = 17145
⇒ x = 635
So, sum lent by Rahul to Sachin
= Rs. ( 1150 + 635 )
= Rs. 1785

$$\eqalign{ & {\text{According to the question,}} \cr & {\text{Principal}} = {\text{Rs}}{\text{. }}2100 \cr & {\text{Amount}} = {\text{Rs}}{\text{. }}2352 \cr & {\text{SI}} = {\text{A}} - {\text{P}} \cr & \,\,\,\,\,\,\, = 2352 - 2100 \cr & \,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}252 \cr & {\text{Time = 2 years,}} \cr & {\text{Let rate = R% }} \cr & {\text{R = }}\frac{{252}}{{2100}} \times \frac{{100}}{2}{\text{ = 6% }} \cr & {\text{New rate of interest}} \cr & {\text{ = (6}} - {\text{1)}} \cr & {\text{ = 5% }} \cr & {\text{New interest}} \cr & {\text{ = }}\frac{{2100 \times 5 \times 2}}{{100}} \cr & {\text{ = Rs}}{\text{. 210}} \cr & {\text{Hence required interest}} \cr & {\text{ = Rs}}{\text{. 210}} \cr} $$

Difference between their rates he gained from both boys
$$\eqalign{ & \Rightarrow (15 \times 5)\% - (12 \times 4)\% \cr & \Rightarrow 75\% - 48\% \cr & \Rightarrow 27\% = 1350{\text{ }}({\text{given)}} \cr & \Rightarrow 100\% = {\text{Rs}}{\text{. 5000}} \cr} $$

According to the question,
Principal + SI for 2 year = Rs. 720 ......(i)
Principal + SI for 7 year = Rs. 1020 ......(ii)
Subtracting equation (i) from (ii)
⇒ SI for 5 years = (1020 - 720) = Rs. 300
⇒ SI for 1 years = Rs. 60
⇒ SI for 2 years = 60 × 2 = Rs. 120
⇒ Principal amount = (Amount after 2 years - 2 years SI) = (720 - 120)
⇒ Principal amount = Rs. 600

Let the amount invested at 12% be Rs. x and that invested at 10% be Rs. y
$$\eqalign{ & \text{Then,} \cr & \to 12\% \,{\text{of }}x + 10\% \,{\text{of }}y = 130 \cr & \Rightarrow 12x + 10y = 13000 \cr & \Rightarrow 6x + 5y = 6500......{\text{(i)}} \cr & {\text{And,}} \cr & \to 10\% \,{\text{of }}x + 12\% \,{\text{of }}y = 134 \cr & \Rightarrow 10x + 12y = 13400 \cr & \Rightarrow 5x + 6y = 6700......{\text{(ii)}} \cr & {\text{Adding (i) and (ii), we get:}} \cr & 11\left( {x + y} \right) = 13200 \cr & \Rightarrow x + y = 1200.......({\text{iii}}) \cr & {\text{Subtracting (i) from (ii),}} \cr & {\text{we get: }} - x + y = 200.......({\text{iv}}) \cr & {\text{Adding (iii) and (iv), }} \cr & {\text{we get}}:2y = 1400\,or\,y = 700 \cr & {\text{Hence,}} \cr & {\text{Amount invested at 12%}} \cr & = \left( {1200 - 700} \right) \cr & = {\text{Rs}}{\text{. 500}} \cr} $$

$$\eqalign{ & {\text{Let each sum}} = {\text{Rs}}{\text{. }}x. \cr & {\text{Let the first sum be invested for}} \cr & \left( {T - \frac{1}{2}} \right){\text{years and}} \cr & {\text{the second sum for }}T{\text{ years}}{\text{.}} \cr & {\text{Then,}} \cr & x + \frac{{x \times 8 \times \left( {T - \frac{1}{2}} \right)}}{{100}} = 2560 \cr & \Rightarrow 100x + 8xT - 4x = 256000 \cr & \Rightarrow 96x + 8xT = 256000....(i) \cr & {\text{And,}} \cr & x + \frac{{x \times 7 \times T}}{{100}} = 2560 \cr & \Rightarrow 100x + 7xT = 256000....(ii) \cr & {\text{From(i) and (ii), we get:}} \cr & 96x + 8xT = 100x + 7xT \cr & \Rightarrow 4x = xT \cr & \Rightarrow T = 4 \cr & {\text{Putting }}T = {\text{4 in (i),we get:}} \cr & 96x + 32x = 256000 \cr & \Rightarrow 128x = 256000 \cr & \Rightarrow x = 2000 \cr & {\text{Hence,}} \cr & {\text{each sum}} = {\text{Rs}}{\text{. 2000}} \cr & {\text{time periods}} = \cr & {\text{4 years and }}3\frac{1}{2}{\text{years}} \cr} $$

According to the question,
$${\text{A}} + \left( {\frac{{{\text{A}} \times {\text{5}} \times {\text{2}}}}{{{\text{100}}}}} \right) = $$     $${\text{B}} + \left( {\frac{{{\text{B}} \times {\text{5}} \times {\text{3}}}}{{{\text{100}}}}} \right) = $$     $${\text{C}} + \left( {\frac{{{\text{C}} \times {\text{5}} \times {\text{4}}}}{{{\text{100}}}}} \right)$$
    110A   =   115B   =   120C
      22A   =     23B   =   24X
Ratio of amount ( by using L.C.M. of 22, 23 and 24)
$$\eqalign{ & {\text{276 : 264 : 253}} \cr & {\text{A's loan = }}\frac{{276}}{{793}} \times {\text{7930}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 2760}} \cr} $$

$$\eqalign{ & {\text{According to the question,}} \cr & {\text{Interest = Rs}}{\text{. 1 per day}} \cr & \therefore {\text{Interest in one year}} \cr & {\text{ = 1}} \times {\text{365 = Rs}}{\text{. 365}} \cr & \therefore {\text{S}}{\text{.I}}{\text{. = }}\frac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{100}} \cr & \Rightarrow 365 = \frac{{{\text{P}} \times 5 \times 1}}{{100}} \cr & \Rightarrow {\text{P}} = \frac{{365 \times 100}}{5} \cr & \Rightarrow {\text{P}} = {\text{Rs}}{\text{. 7300}} \cr} $$

$$\eqalign{ & {\text{According to the question,}} \cr & {\text{Amount = Rs}}{\text{. 3144}} \cr & {\text{Rate = 8}}\% \cr & {\text{Let, Principal = Rs}}{\text{. }}x \cr & \therefore {\text{Time = }} \cr & \frac{{30 + 29 + 31 + 30 + 31 + 30 + 31 + 7}}{{366}} \cr & = \frac{{219}}{{366}} \cr & \therefore {\text{SI = }}\frac{{{\text{P}} \times {\text{R}} \times {\text{T}}}}{{100}} \cr & \Rightarrow 3144 - x = \frac{{x \times 8 \times 219}}{{100 \times 366}} \cr & = {\text{Rs}}{\text{. 3000}} \cr & \cr & {\bf{Alternate}} \cr & \Rightarrow {\text{P}} + \frac{{{\text{P}} \times 8 \times \frac{{219}}{{365}}}}{{100}} = 3144 \cr & \Rightarrow {\text{P}} + \frac{{{\text{P}} \times 8 \times \frac{3}{5}}}{{100}} = 3144 \cr & \Rightarrow 100{\text{P}} + \frac{{24{\text{P}}}}{5} = 314400 \cr & \Rightarrow \frac{{524{\text{P}}}}{5} = 314400 \cr & \Rightarrow {\text{P = }}\frac{{314400 \times 5}}{{524}} \cr & \Rightarrow {\text{P}} = {\text{600}} \times {\text{5}} \cr & \Rightarrow {\text{P = Rs}}{\text{.}} \, 3000 \cr} $$

Let the rates of interest in the former and latter cases be R% and (R + 1) % p.a.
Then,
$$\eqalign{ & 5000 \times {\text{R}} \times 4 = 4000 \times \left( {{\text{R}} + 1} \right) \times 4 \cr & \Rightarrow \frac{{{\text{R}} + 1}}{{\text{R}}} = \frac{{5000 \times 4}}{{4000 \times 4}} \cr & \Rightarrow 1 + \frac{1}{{\text{R}}} = 1 + \frac{1}{4} \cr & \Rightarrow {\text{R}} = 4 \cr & {\text{Hence,}} \cr & {\text{Required rate}} = 4\% \,{\text{p}}{\text{.a}}{\text{.}} \cr} $$