A father divide Rs. 1,301 between his sons - Bhavya and Aakash. He asked them to invest it at 4% rate of interest compounded annually. It was seen that Bhavya and Aakash got the same amount after 11 and 13 years respectively. How much did father gave to Bhavya?
Answers
Step-by-step explanation:
suppose amount of A = x
so amount of B = 1301 -x (because all amount is 1301)
As question x(1+\frac{4}{100}) ^{7}= 1301-x(1+\frac{4}{100}) ^{9}x(1+
100
4
)
7
=1301−x(1+
100
4
)
9
= x(\frac{104}{100}) ^{7} = 1301-x(\frac{104}{100}) ^{9}x(
100
104
)
7
=1301−x(
100
104
)
9
(transtion)
= \frac{x}{1301-x} =(\fra\left \{ {{\frac{104}{100}^{9}} \atop {\frac{104}{100}^{7}}} ) (same base so power to rest)
=\frac{x}{1301-x} =(\frac{104}{100}) ^{2}
1301−x
x
=(
100
104
)
2
= \frac{x}{1301-x} =\frac{26X26}{25X25}
1301−x
x
=
25X25
26X26
(on the transition)
= \frac{x}{1301-x} =\frac{676}{625}
1301−x
x
=
625
676
625x=(1301-x) X 676
625x = (1301X676) - 676x
= 676x + 625x = 1301X676 ( on the transition)
1301x = 1301 X 676
x = 676
so 1301-x = 625
