The rate of simple interest reduces from 4% to 31/4% and for this the annual income decreases by Rs60.What is the principle?
Answers
Answer:
let the principle amount be ₹x,
Simple interest at 4% in 1years(let)=
\frac{p \times r \times t}{100}
100
p×r×t
= > \frac{x \times 4 \times 1}{100}=>
100
x×4×1
= > \frac{x}{25}=>
25
x
Amount=S.I.+principle
= \frac{x}{25} + x=
25
x
+x
= \frac{26x}{25}=
25
26x
Now,
simple interest at 15/4% in 1years=
= \frac{x \times 4\times 1}{5\times 100}=
5×100
x×4×1
= > \frac{x}{125}=>
125
x
Amount=
\frac{x}{125} + x
125
x
+x
= \frac{126x}{125}=
125
126x
According to question,
Amount at 4%-₹60=Amount at 5/4%
= > \frac{26x}{25} - 60 = \frac{126x}{125}=>
25
26x
−60=
125
126x
= > \frac{26x - 1500}{25} = \frac{126x}{125}=>
25
26x−1500
=
125
126x
multiple both the side by 25 we get:
= > \frac{26x - 1500}{25} \times 25 = \frac{126x}{125} \times 25=>
25
26x−1500
×25=
125
126x
×25
= > 26x - 1500 = \frac{126x}{5}=>26x−1500=
5
126x
Cross multiplying:
= > 130x - 7500 = 126x=>130x−7500=126x
Transposing:
= > 130 x - 126x = 7500=>130x−126x=7500
= > 4x = 7500=>4x=7500
= > x = \frac{7500}{4}=>x=
4
7500
= > x = 1875rupes=>x=1875rupes
Principle=₹1875
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