Answer

Solution

UPSC Prelims

Mathematics

Theme:

Elementary Algebra / प्रारंभिक बीजगणित

Q59 2021, Elementary Algebra

Consider the following addition problem: 3P+4P+PP+PP = RQ2; where P, Q and R are different digits. What is the arithmetic mean of all such possible sums?

निम्नलिखित जोड़ (एडिशन) के प्रश्न पर विचार कीजिए : 3P+4P+PP+PPRQ2; जहाँ P, Q तथा R भिन्न अंक है। इन सभी संभाव्य योगफलों का समांतर माध्य क्या है?

Explanation Please wait..

3P + 4P + PP + PP = RQ2

Or 30 + P + 40 + P + 10P + P + 10P + P = 100R + 10 Q + 2

Or 24P + 70 = 100R + 10 Q + 2

Or 20P + 70 + 4P = 100R + 10 Q + 2.

The unit digit of the resultant is 2.

It will be obtained when 4 is multiplied by P.

So, P must be 3, or 8. If P = 3, then: 24P + 70 = 24 × 3 + 70 = 72 + 70 = 142.

If P = 8, then: 24P + 70 = 24 × 8 + 70 = 192 + 70 = 262.

Arithmetic sum of 142 and 262 = (142 + 262)/2 = 202.

व्याख्या Please wait..

Question Meta

ID:

Year:

Q.No:

Source:

Draft Mode v1.2

Solving Technique

Type Of MCQ

0

EN Question Title

0

ह Hindi Title

0