Question

Ashok borrowed ₹12,000 at some rate on compound interest. After a year, he paid back ₹4,000. If the compound interest for the second year is ₹920, find:

i. The rate of interest charged

ii. The amount of debt at the end of the second year

In easy method ​

Answer 1

Answer:

Loan = Rs 12,000 Interest rate = r % compound

Amount after one year = Rs 12,000 ( 1 + r/100) = Rs 120 (100+r)

Amount paid back after one year = Rs 4,000

Balance Amount in the loan = Rs 120 (100+r) - 4,000 = Rs (8,000 + 120 r)

Compound Interest for 2nd year turns out to be same as simple interest on the above amount: \begin{gathered}Rs\ (8000+ 120 r) * r / 100 = Rs\ 80\ r +1.2 r^2 \\ \\1.2\ r^2 + 80\ r = 920 \\ \\ r = \frac{-80 +- \sqrt{80^2+4*920*1.2}}{1.2 * 2} \\ \\ r = (-80+104)/2.4 = 10 \\ \\\end{gathered}

Rs (8000+120r)∗r/100=Rs 80 r+1.2r

2

1.2 r

2

+80 r=920

r=

1.2∗2

−80+−

80

2

+4∗920∗1.2

r=(−80+104)/2.4=10

Rate of interest is 10% (we ignore the negative root of quadratic equation)

2)

\begin{gathered}Amount\ after\ 2\ years : Rs (8,000 + 120 r ) + Rs (80 r + 1.2 r^2) \\ \\ = Rs 8,000+ 200 r + 1.2 r^2 \\ \\ = Rs\ 8,000 + 200*10+1.2*100 = Rs\ 11,200.\end{gathered}

Amount after 2 years:Rs(8,000+120r)+Rs(80r+1.2r

2

)

=Rs8,000+200r+1.2r

2

=Rs 8,000+200∗10+1.2∗100=Rs 11,200.

Answer 2

Step-by-step explanation:

★Given -

AB · CD = BC · DA.

∠XAB = ∠XCD and ∠XBC = ∠XDA.

★To prove -

∠BXA + ∠DXC = 180⁰

★Concept -

Here, we'll use the concept of congruency to solve the question. Let's do it!!

★Solution -

\rm{∠XAB = ∠XCD } \: \: \: \: \: (given)∠XAB=∠XCD(given)

=> AB || CD (converse of alternate interior angles)

\rm{∠XBC = ∠XDA } \: \: \: \: \: (given)∠XBC=∠XDA(given)

=> BC || DA (converse of alternate interior angles)

∴ ABCD is a parallelogram (opposite pair of sides are parallel)

AB · CD = BC · DA (given)

=> AB · AB = BC · BC

=> AB² = BC²

Taking square root on both sides, we get,

AB = BC

Hence, ABCD is a rhombus (adjacent sides are equal)

∠BXA = 90⁰ (diagonals of a rhombus bisect each other at right angles)------(1)

∠DXC = 90⁰ (diagonals of a rhombus bisect each other at right angles)------(2)

(1) + (2),

\rm{ \longmapsto ∠BXA + ∠DXC = 90⁰ + 90⁰}⟼∠BXA+∠DXC=90⁰+90⁰

\rm{ \longmapsto {\bf\orange{ ∠BXA + ∠DXC = 180⁰}}}⟼∠BXA+∠DXC=180⁰

★More to know -

A convex quadrilateral is a quadrilateral having all its interior angles measuring less than 180°.

A convex quadrilateral has both diagonals inside the figure.

A Rectangle, a rhombus, a parallelogram are examples of convex quadrilateral.