Answer :
Let the sum be x
case (i)
Principle = x, Rate = 7%, time = 3.5 yrs
Interest = [tex] \frac{PTR}{100} [/tex]
= [tex] \frac{x (7)(3.5)}{100} [/tex]
= [tex] \frac{24.5x}{100} [/tex]
case (ii)
Principle = x, Rate = 5%, time = 4 yrs
Interest = [tex] \frac{PTR}{100} [/tex]
= [tex] \frac{x (5)(4)}{100} [/tex]
= [tex] \frac{20x}{100} [/tex]
given that, the simple interest for case (i) is Rs 225 more than the simple interest for case (ii)
[tex]\frac{24.5x}{100} - \frac{20x}{100} = 225[/tex]
[tex] \frac{4.5x}{100} [/tex] = 225
x = [tex] \frac{22500}{4.5} [/tex]
x = 5000
The sum = Rs 5000
case (i)
Principle = x, Rate = 7%, time = 3.5 yrs
Interest = [tex] \frac{PTR}{100} [/tex]
= [tex] \frac{x (7)(3.5)}{100} [/tex]
= [tex] \frac{24.5x}{100} [/tex]
case (ii)
Principle = x, Rate = 5%, time = 4 yrs
Interest = [tex] \frac{PTR}{100} [/tex]
= [tex] \frac{x (5)(4)}{100} [/tex]
= [tex] \frac{20x}{100} [/tex]
given that, the simple interest for case (i) is Rs 225 more than the simple interest for case (ii)
[tex]\frac{24.5x}{100} - \frac{20x}{100} = 225[/tex]
[tex] \frac{4.5x}{100} [/tex] = 225
x = [tex] \frac{22500}{4.5} [/tex]
x = 5000
The sum = Rs 5000
Step-by-step explanation:
Let the principle be Rs. 100 in both the cases
SI for 3½ or 7/2 years at 7%=P*R*T/100 =100*7*7/2/100
=49/2
=Rs.24.5
SI for 4 years at 5%=100*5*4/100
=Rs.20
The difference is=Rs.24.5-Rs.20
=Rs.4.5
If the difference is Rs.4.5,the principal=Rs.100
If the difference is Rs.225,the principal
=100/4.5*225
=100*10*225/45
=Rs.5000
so,Rs.5000 was the sum in both the cases
Hope it helps