If the digits of one of the nine two-digit numbers are interchanged,…
If the digits of one of the nine two-digit numbers are interchanged, then the average of these numbers decreases by 6. Find the difference between the digits of the number whose digits have been interchanged.
यदि नौ दो-अंकीय संख्याओं में से एक संख्या के अंकों को आपस में बदल दिया जाए, तो इन संख्याओं का औसत 6 कम हो जाता है। उस संख्या के अंकों का अंतर ज्ञात कीजिए।
Detailed Solution & Logic
06
Solution
मान लेते हैं संख्या के अंक a और b हैं।
मूल संख्या = 10a+b
अंक बदलने पर नई संख्या = 10b+a
अंतर:
(10a+b)-(10b+a)=9(a-b)
औसत 6 कम हुआ और कुल 9 संख्याएँ हैं, इसलिए कुल योग में कमी:
$6\times9=54$
इसलिए:
9(a-b)=54
a-b=6
अतः अंकों का अंतर 6 है।
✅ सही उत्तर: 06
Similar Practice Questions
The ratio of the length to the breadth of a school playground is 5 : 2. If the breadth is 40 meters, what is the length?
The ratio of the length to the breadth of a school playground is 5 :...
What is the cost price of an article
What is the cost price of an article which is sold for ₹1,566 with 8%...
Amit invests a sum of ₹5400
Amit invests a sum of ₹5400 and Gopal invests a sum of ₹9400 at the...
Two pipes A and C can fill a tank in 10 hours and 15 hours respectively.
Two pipes A and C can fill a tank in 10 hours and 15 hours...
A car covers four successive 8 km distances
A car covers four successive 8 km distances at speeds of 12 km/hr, 18 km/hr,...
The population of a village is 12,000. If it increases by 10% the first year and decreases by 5% the next year, what is the population after 2 years?
The population of a village is 12,000. If it increases by 10% the first year...
The average age of 48 students of a class is 22 years.
The average age of 48 students of a class is 22 years. If the age...