संख्याएँ A, B और C का औसत 60 है। यदि A और B के योग का C के योग से अनुपात 7:2 है, तो B का मान ज्ञात कीजिए। दिया गया है कि A का मान, B से 20 अधिक है।

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  1. 40
  2. 80
  3. 90
  4. 100
  5. 60

Answer (Detailed Solution Below)

Option 5 : 60
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दिया गया है:

A, B और C का औसत = 60

A और B के योग का C से अनुपात 7:2 है।

A, B से 20 अधिक है।

गणना:

A, B और C का औसत = (A + B + C) / 3 = 60

A + B + C = 60 x 3 = 180

यह भी दिया गया है कि (A + B) / C = 7 / 2. इसलिए:

A + B = (7 / 2) × C

A = B + 20 से, इस समीकरण में प्रतिस्थापित करें A + B = (7 / 2) × C:

(B + 20 + B) = (7 / 2) × C

2B + 20 = (7 / 2) × C

अब, हम यह भी जानते हैं कि A + B + C = 180 है, A = B + 20 को इस समीकरण में प्रतिस्थापित करें:

(B + 20) + B + C = 180

2B + 20 + C = 180

C = 180 - 2B - 20

C = 160 - 2B

अब C = 160 - 2B को समीकरण 2B + 20 = (7 / 2) × C में प्रतिस्थापित करें:

2B + 20 = (7 / 2) × (160 - 2B)

2B + 20 = 560 - 7B

2B + 7B = 560 - 20

9B = 540

B = 540 / 9 = 60

इसलिए, B का मान 60 है।

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