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Direct and Inverse Proportions | Exercise 13.1

Question 18

Q9) A 5m 60cm high vertical pole casts a shadow 3m 20= long. Find at the same time (i) the length of the shadow cast another pole 10m 50cm high (ii) the height of a pole which casts a shadow 5m long.

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Solution (i):

Let the length of the shadow of the other pole be x m.

1m = 100cm

The given information in the form of a table is as follows.

More the height of an object, more will be the length of its shadow.

Thus, the height of an object and length of its shadow are directly proportional to each other. therefore, we obtain.

\frac{5.60}{3.20}=\frac{10.50}{x}

\Rightarrow x=\frac{10.50\times3.20}{5.60}=6

Hence, the length of the shadow will be 6 m.

Solution (ii):

Let the height of the pole be y m.

The given information in the form of a table is as follows.

The height of the pole and length of the shadow are directly proportional to each other. Therefore,

\frac{5.60}{3.20}=\frac{y}{5}

y=\frac{5\times5.60}{3.20}=8.75

Thus, the height of the pole is 8.75 m.

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Our top 5% students will be awarded a special scholarship to Lido.

subject-cta

Question 18

Q9) A 5m 60cm high vertical pole casts a shadow 3m 20= long. Find at the same time (i) the length of the shadow cast another pole 10m 50cm high (ii) the height of a pole which casts a shadow 5m long.

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

Solution (i):

Let the length of the shadow of the other pole be x m.

1m = 100cm

The given information in the form of a table is as follows.

More the height of an object, more will be the length of its shadow.

Thus, the height of an object and length of its shadow are directly proportional to each other. therefore, we obtain.

\frac{5.60}{3.20}=\frac{10.50}{x}

\Rightarrow x=\frac{10.50\times3.20}{5.60}=6

Hence, the length of the shadow will be 6 m.

Solution (ii):

Let the height of the pole be y m.

The given information in the form of a table is as follows.

The height of the pole and length of the shadow are directly proportional to each other. Therefore,

\frac{5.60}{3.20}=\frac{y}{5}

y=\frac{5\times5.60}{3.20}=8.75

Thus, the height of the pole is 8.75 m.

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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