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The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. A prize money of Rs. 31800 was distributed between Aman, Bipin and Chetan. Find the share received by Chetan. I) The ratio of their shares is 18 ∶ 15 ∶ 20 respectively. II) Aman received 20% more than Bipin, but 10% less than Chetan. III) Bipin received 5/6 of Aman’s share and 3/4 of Chetan’s share.

The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. A prize money of Rs. 31800 was distributed between Aman, Bipin and Chetan. Find the share received by Chetan. I) The ratio of their shares is 18 ∶ 15 ∶ 20 respectively. II) Aman received 20% more than Bipin, but 10% less than Chetan. III) Bipin received 5/6 of Aman’s share and 3/4 of Chetan’s share. Correct Answer Any one

Considering statement I,

Sum of ratios = 18 + 15 + 20 = 53

Chetan’s share = (20/53) × 31800 = Rs. 12000

Considering statement III,

Aman’s share = (100 + 20) % of Bipin’s share = 1.2 × Bipin’s share

Also, Aman’s share = (100 - 10) % of Chetan’s share = 0.9 × Chetan’s share

Equating the above equations, we get,

⇒ 1.2 × Bipin’s share = 0.9 × Chetan’s share

⇒ Bipin’s share = 0.75 × Chetan’s share

Now, Aman’s share + Bipin’s share + Chetan’s share = 31800

⇒ 0.9 × Chetan’s share + 0.75 × Chetan’s share + Chetan’s share = 31800

⇒ 2.65 × Chetan’s share = 31800

⇒ Chetan’s share = 31800/2.65 = Rs. 12000

Considering statement II,

Bipn’s share = 5/6 × Aman’s share

Also, Bipin’s share = 3/4 × Chetan’s share

Equating the above equations, we get,

⇒ 5/6 × Aman’s share = 3/4 × Chetan’s share

⇒ Aman’s share = 9/10 × Chetan’s share

Now, Aman’s share + Bipin’s share + Chetan’s share = 31800

⇒ 9/10 × Chetan’s share + 3/4 × Chetan’s share + Chetan’s share = 31800

⇒ 53/20 × Chetan’s share = 31800

⇒ Chetan’s share = Rs. 12000

∴ The question can be answered using any one of the given statements

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