We have 
\(4\frac { 2 }{ 3 } -3\frac { 1 }{ 4 } +2\frac { 1 }{ 6 } \)=\(\frac { 14 }{ 3 } -\frac { 13 }{ 4 } +\frac { 13 }{ 6 } \)
= \(\frac { 14\times 4 }{ 3\times 4 } -\frac { 13\times 3 }{ 4\times 3 } +\frac { 13\times 2 }{ 6\times 2 } \)
∵ LCM of 3, 4 and 6 is 12, so we convert each fraction into an equivalent fraction with denominator 12
i,e  \(\frac { 56 }{ 12 } -\frac { 39 }{ 12 } +\frac { 26 }{ 12 } =\frac { 56-39+26 }{ 12 } \)
= \(\frac { 82-39 }{ 12 } =\frac { 43 }{ 12 } =3\frac { 7 }{ 12 } \)

(a) No. of students like to study English
= \(\frac { 1 }{ 5 } \times 40\)
= 8
(b) No. of students like to study Maths
= \(\frac { 2 }{ 5 } \times 40\)
= 2\(\times\) 8
= 16
(c) No. of students who like to study Science
=40 - (8 + 16)
= 40-24
= 16
In part (ii), we know
\(\frac { 2 }{ 5 } \times 40\) = 16
So,\(\frac { 2 }{ 5 } \)of the total number of students like to study Science

Total hours spend by Ritika for studies =11\(\frac { 1 }{ 3 } \) hours =\(\frac { 34 }{ 3 } \)hours
 Total hours devoted by Ritika for Hindi and Sanskrit 5\(\frac { 3 }{ 5 } \)= \(\frac { 28 }{ 5 } \)hours
Total hours devoted by Ritika for other subjects
= \(\frac { 34 }{ 3 } -\frac { 28 }{ 5 } \)
= \(\frac { 170-84 }{ 15 } =\frac { 86 }{ 15 } \)
=5\(\frac { 11 }{ 15 } \) hours

2

169.86 m²

We have
Cost of 1 kg of sugar = Rs.17\(\frac { 3 }{ 4 } \)=Rs\(\frac { 71 }{ 4 } \)k
∴ Cost of 8 kg of sugar = Rs \(\left( \frac { 71 }{ 4 } \times 8\frac { 1 }{ 2 } \right) \)
=Rs \(\left( \frac { 71 }{ 4 } \times \frac { 17 }{ 2 } \right) =Rs.\left( \frac { 71\times 17 }{ 4\times 2 } \right) \)
=Rs\(\left( \frac { 1207 }{ 8 } \right) \) =Rs.150\(\frac { 7 }{ 8 } \)
Hence, the cost of 8\(\frac { 1 }{ 2 } \) kg of sugar is Rs.150\(\frac { 7 }{ 8 } \)

\(\frac{1}{12}\)

\(\frac{6}{27}\)

2500 stamps

\(\frac{1}{4}\)