Question

A 5m 60cm high vertical pole casts shadow 3m 20cm long. Find at the same time.
1.the length of the Shadow cast by another pole 10m 50cm hight
2.the height of a pole which casts a shadow 5M long.​

Answer 1

Given :

A 5m 60cm high vertical pole casts shadow 3m 20cm long.

To find :

• The length of the Shadow cast by another pole 10m 50cm height
• The height of a pole which casts a shadow 5m long.

Solution :

• Convert 'cm' into 'm'

Height of vertical pole = 5m60cm

★ 1m = 100cm

→ 5 + 60/100

→ 5 + 0.6 = 5.6 m

Length of the shadow = 3m20cm

→ 3 + 20/100

→ 3 + 0.2

→ 3.2m

Length of the shadow cast by another pole

→ 10m50cm

→ 10+ 50/100

→ 10 + 0.5 = 10.5m

Solve such type of problem by indirect and direct proportion.

• ★ First case

The length of the Shadow cast by another pole 10m 50cm height

• It's a case of direct proportion

Consider the length of the shadow be y

________________________________

Height of pole 5.6m 1.5m

________________________________

Length of shadow 3.2m y

________________________________

→ 5.6/3.2 = 10.5/y

→ 56/32 = 10.5/y

→ 7/4 = 10.5/y

→ 7y = 4 × 10.5

→ 7y = 42

→ y = 42/7

→ y = 6 m

•°• Length of shadow cast by another pole is 6m

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• ★ Second case

The height of a pole which casts a shadow 5m long.

• It's a case of direct proportion

Consider the height of pole be x

________________________________

Height of pole 5.6m x

________________________________

Length of shadow 3.2m 5

________________________________

→ 5.6/3.2 = x/5

→ 56/32 = x/5

→ 7/4 = x/5

→ 7 × 5 = 4x

→ 4x = 35

→ x = 35/4

→ x = 8.75 m

•°• The height of pole is 8.75m

━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

$\Large{\bf{Given\::}}$

• Height of a vertical pole is 5m 60cm.

⇢ 5m 60cm

⇢ (5 × 100)cm + 60cm

⇢ 500cm + 60cm

⇢ 560 cm

• Height of shadow is 3m 20cm.

⇢ 3m 20cm

⇢ (3 × 100)cm + 20cm

⇢ 300cm + 20cm

⇢ 320 cm

$\\ \Large{\bf{To\: Find\::}}$

⠀⠀ ❶ The length of the shadow cast by another pole of height 10m 50cm.

⠀ ⠀❷ The height of a pole which casts a shadow 5m long.

$\\ \Large{\bf{Solution\::}}$

We know that,

➣ As height of pole increases, length of shadow also increases.

Case - 1 :

Given that,

• Height of the pole is 10m 50cm.

⇢ 10m 50cm

⇢ (10 × 100)cm + 50cm

⇢ 1000cm + 50cm

⇢ 1050 cm

Now,

➠ 560 cm pole casts 320 cm shadow.

➠ 1 cm pole casts $\tt{\left(\dfrac{320}{560}\right)}$ cm shadow.

➠ 1050cm pole casts $\tt{\left(\dfrac{320}{560}\times{1050}\right)cm}$ shadow.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= $\tt{\left(\dfrac{32}{56}\times{1050}\right)}$ cm

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= (32 × 18.75) cm

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 600 cm ≈ 6 m

∴ The length of the shadow cast by another pole of height 10m 50cm is 6 m.

Case - 2 :

Given that,

• Height of the shadow is 5 m.

⇢ 5m

⇢ (5 × 100) cm

⇢ 500 cm

Again,

➠ 320 cm shadow cast by 560 cm pole.

➠ 1 cm shadow cast by $\tt{\left(\dfrac{560}{320}\right)}$ cm pole.

➠ 500cm )) cast by $\tt{\left(\dfrac{560}{320}\times{500}\right)cm}$ pole.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= $\tt{\left(\dfrac{56}{32}\times{500}\right)}$ cm

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= (56 × 15.625) cm

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 875 cm ≈ 8.75 m

∴ The height of a pole which casts a shadow 5m long is 8.75 m.

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