Amar is an electrician. He bought $7\dfrac{1}{2}$ bundles of an electric cable where each bundle had $202\dfrac{4}{5}$ m of cable.

(1) Find the total length of the cable purchased by Amar.

1. 1427 m
2. 1521 m
3. 1605 m
4. 1717 m

(2) If the cost of cable is ₹$6\dfrac{2}{3}$ per metre, find the amount paid by Amar.

1. ₹8830
2. ₹9520
3. ₹10140
4. ₹11280

(3) Amar used $2\dfrac{1}{2}$ bundles of cable for electric connections in the top floor of the building. What length of cable was used for the top floor ?

1. 476 m
2. 507 m
3. 625 m
4. 712 m

(4) Amar cut a length of $13\dfrac{4}{5}$m from a bundle and divided the remaining cable of this bundle into pieces of 21 m, length each. How many pieces of 21 m did he get from this bundle ?

1. 9
2. 10
3. 11
4. 12

(1) Given:

Total bundles = $7 \dfrac{1}{2} = \dfrac{15}{2}$

Length per bundle = $202 \dfrac{4}{5} = \dfrac{1014}{5}$ m

Total length of the cable purchased = (Total bundles) x (Length per bundle)

Substituting the values in above, we get:

Total length of the cable purchased = $\dfrac{15}{2}$ x $\dfrac{1014}{5}$ m

= $\dfrac{3}{2}$ x $\dfrac{1014}{1}$ m

= $\dfrac{3}{1}$ x $\dfrac{507}{1}$ m

= 1521 m

Hence, option 2 is the correct option.

(2) The cost of cable per meter = ₹$6\dfrac{2}{3} = ₹\dfrac{20}{3}$ $\hspace{2cm}$

Given

Total length of the cable = 1521 m $\hspace{2.5cm}$ [From previous step]

The amount paid by Amar = (Cost of cable per meter) x (Total length of the cable)

Substituting the values in above, we get:

The amount paid by Amar = ₹$\dfrac{20}{3}$ x 1521 m

= ₹20 x 507

= ₹10140

Hence, option 3 is the correct option.

(3) Given:

Bundles of cable used for the top floor = $2\dfrac{1}{2} = \dfrac{5}{2}$

Length per bundle = $\dfrac{1014}{5}$ m

Length of cable used for the top floor = (Bundles of cable used for the top floor) x (Length per bundle)

Substituting the values in above, we get:

Length of cable used for the top floor = $\dfrac{5}{2}$ x $\dfrac{1014}{5}$ m = 507 m

Hence, option 2 is the correct option.

(4) Given:

Length of one bundle = $\dfrac{1014}{5}$ m

Cut length = $13\dfrac{4}{5}$ m = $\dfrac{69}{5}$ m

Remaining length = (Length of one bundle - Cut length)

Substituting the values in above, we get:

Remaining length = $\Big(\dfrac{1014}{5} - \dfrac{69}{5}\Big)$ m

= $\dfrac{1014 - 69}{5}$ m = $\dfrac{945}{5}$ m = 189 m

Number of pieces of 21 m length = Remaining length ÷ 21

Substituting the values in above, we get:

Number of pieces of 21 m length = 189 m ÷ 21 = $\dfrac{189}{21}$

= 9

Hence, option 1 is the correct option.