P.W. = Rs. (1760 -160) = Rs. 1600.

So, S.I. on Rs. 1600 at 12% is Rs. 160.

Therefore Time = \(\left(\frac{100\times160}{1600\times12}\right) =\frac{5}{6} years = \left(\frac{5}{6}\times12\right)months = 10 months.\)

P.W. = Rs. \(\left[\frac{100\times2310}{100+\left(15\times\frac{5}{2}\right)}\right] = Rs.1680.\)

S.I. on Rs. (260 - 20) for a given time = Rs. 20.

S.I. on Rs. 240 for half the time = Rs. 10.

T.D. on Rs. 250 = Rs. 10.

Therefore T.D. on Rs. 260 = Rs. \(\left(\frac{10}{250}\times260\right) = Rs. 10.40\)

S.I. on Rs. 750 = T.D. on Rs. 960.

This means P.W. of Rs. 960 due 2 years hence is Rs. 750.

So,  T.D. = Rs. (960 - 750) = Rs. 210.

Thus, S.I. on R.s 750 for 2 years is Rs. 210.

So, Rate =    \(\left(\frac{100\times210}{750\times2}\right)\)  %  = 14%

Sum = \(\frac{S.I\times T.D}{(S.I.)-(T.D.) }= \frac{85\times80}{(85-80)} =Rs. 1360\)

Required sum = P.W. of Rs. 702 due 6 months + P.W. of Rs. 702 due 1 year hence

= Rs. \(\left[\left(\frac{100\times702}{100+8\times\frac{1}{2}}\right)+\left(\frac{100\times702}{100+(8\times1)}\right)\right]\)

= Rs. (675 + 650)

= Rs. 1325.

P.W. = \(\frac{100\times T.D.}{R\times T} = \frac{100\times168}{14\times2} = 600.\)

So, Sum = (P.W. + T.D.) = Rs. (600 + 168) = Rs. 768.

T.D.   =  \(\frac{B.D.\times 100}{100+(R\times T)}\)

= Rs.\(\left[\frac{420\times100}{100+\left(15\times\frac{1}{3}\right)}\right]\)

=Rs.  \(\left(\frac{420\times100}{105}\right)\)

= Rs.400.

S.I. on Rs. 1600 = T.D. on Rs. 1680.

So, Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.

So, Time = \(\left(\frac{100\times80}{1600\times15}\right)year = \frac{1}{3}year = 4 months.
\)

T.D.  = \(\left(\frac{B.G\times100}{Rate\times Time}\right) = Rs.\left(\frac{24\times100}{10\times100}\right) = Rs.120.\)

Therefore p.w. = \(\left(\frac{100\times T.D.}{Rate\times Time}\right) = Rs.\left(\frac{100\times120}{10\times100}\right) = Rs.600.\)