Question
The mean of five two-digit
numbers is 34. Among these five numbers, two are 'P' and 'Q'. If the digits of both 'P' and 'Q' are swapped, the new mean of the five numbers changes to 14.2. Alternatively, if the other three numbers (excluding 'P' and 'Q') are multiplied by '−1', the mean of the five numbers becomes 10. What is the sum of the tens digits of 'P' and 'Q'?Solution
ATQ,
Let, P = 10a + b, Q = 10c + d & Sum of other 3 numbers = R Given P + Q + R = 34 × 5 = 170 --- (1) P + Q – R = 10 × 5 = 50 --- (2) Solving equation 1 & 2, we have, P + Q = (170 + 50)/2 = 110, So, R = 170 – 110 = 60 & (10a + b) + (10c + d) = 110 (b + d) = 110 – 10(a + c) --- (3) Again, given that, (10b + a) + (10d + c) + R = 5 × 14.2 (10b + a) + (10d + c) + 60 = 71 (10b + a) + (10d + c) = 11 10(b + d) + (a + c) = 11 10[110 – 10(a + c)] + (a + c) = 11 1100 – 100(a + c) + (a + c) = 11 99(a + c) = 1089 (a + c) = 11 = Sum of tens digit
Article ‘P’, if sold at a profit of 30% earns a profit of Rs. 510. If article ‘P’ is marked 60% above its cost price and then sold after offerin...
If there is a loss of 20% on selling the article at 16/25 of the original selling price then what will be the percentage profit after selling the articl...
A shopkeeper sold an article at marked price and got a profit of 70%. If he had given a discount of 30%, then find his new profit percent.
A trader sells pulses at a 32% profit and uses weights 20% less than the actual measure. Find his gain percentage.
A shopkeeper bought 60 pencils at a rate of 4 for Rs. 5 and another 60pencils at a rate of 2 for Rs.3. He mixed all the pencils and sold them at a rate ...
A jeweler sells a necklace for Rs. 4000 with a 25% profit and a bracelet for Rs. 1200 with a 20% profit. If the necklace is sold for Rs. 3500, what is t...
Charan went to purchase an Apple iPhone, the shopkeeper told him to pay 30% GST, if he asked the bill. Charan manages to get the discount of 10% on the...
A dishonest dealer announces selling his articles with a 25% loss but uses 40% lighter weights. What is the percentage of his profit or loss?
A bought an article at 20% less of the marked price and sold it at 10% more than the marked price. Find the profit earned by him.
A, B and C started a business. Twice the investment of A is equal to thrice the investment of B and also five times the investment of C. If the total pr...
Relevant for Exams:
