What is the sum of all the four digit number formed by the digits 1, 2, 5, 6 (without repetition)?
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Solution
Keeping 6 as the 1st digit we can arrange the remaining numbers in 3! ways is 6 ways
∴ starting with 6 we will have 6 numbers Similarly we can have 6 numbers each starting with 1,2 and 5
∴ Count of tour digit number formed = 24
24 numbers formed from 4 digits i.e. each digit appears 6 times in each of the places (units, tens, hundreds and thousands)
∴ sum of digits of the row = 6( 1 + 2 + 5 + 6) = 84
Considering place value; sum of rows is
Thousand Hundreds Ten Units
84000 8400 840 84
∴ Sum of all numbers formed is 84000 + 8400 + 8400 + 84 = 93324
What is the sum of angles A, B, C, D, & E?
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Solution
Sum of angles of a n point star is = (π - 4)* π
In this case, n = 5
∴ Sum of angles; (5 - 4)* π
= π = 180
A salesman gets commission on total sales at 9%. If the sale exceeds $10,000, he gets an additional commission of 3%. If he gets a total of $1380 as commission, then what is the amount of bonus received?
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Solution
On $10000 he will get commission of $900.
Additional commission is $1380 - $900 = $480
∴ Additional sale = \(\frac{\$ 480}{9+3}\) x 100 = \(\frac{\$ 480}{12}\) x 100 = $4000
Additional commission on $4000 @3%= $120
In a race of 500 metres, X runs at 5 metres per second. If X gives Y a start of 20 metres and still beats him by 20 seconds, what is speed of Y?
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Solution
Time taken by x =\(\frac{500\, metres}{5}\)= 100 seconds.
Y runs only 480 metres and takes 20 seconds more than x i.e. 120 seconds
480 meters Speed of y =\(\frac{480\, meters}{120\, seconds}\)= 4 metres per second
A gives B, a start of 30m or 10 seconds and they both finish the race of 1km at the same time. What is the speed B?
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Solution
B either starts the race 30 metres ahead of A or 10 seconds before A to complete the race at the same time.
In 10 seconds B runs, 30 metres
In 3600 seconds B runs 10800 metres
(Speed 10.8 kmph)
In a village, the average age of n people is 42 years. But after verification it was found that the age of a person had been considered 20 years less than the actual age; so the new average age after correction increases by 1. What is the value of n?
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Solution
Total age = No. of people x Average
= n x 42
= 42n
After verification;
Total age = 42n + 20
New average = 42 + 1= 43
∴ \(\frac{42n+20}{n}\) = 43
42n+20 = 43n
n = 20
30 workers can finish a job in 20 days after how many days should 9 workers leave the job so that the work is completed in a total of 26 days?
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Solution
Let the total amount of work be 600 units
∴ Efficiency of 1 worker = 1 unit
Worker 30 21
Days X 26-x
Total work done 30 x 21 (26 - x)
But total work = 600
⇒ 30x + 21(26-x) = 600
30x + 546 - 21x = 600
X = 6 days
A can complete a job in 10 days, Bin 12 days. Find the time taken by them when A and B worked alternatively, starting with B
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Solution
B can complete \(\frac{1}{12}\) the Job in 1 day
A can complete \(\frac{1}{10}\) the job in 1 day
B and then A can complete \(\frac{1}{12}+\frac{1}{10}=\frac{11}{30}\) job in 2 days
B and then A can complete \(\frac{55}{60}\) job 10 days
Then B will complete the remaining \(\frac{5}{60}\) job on the 11th day
Ans is 11 days
A trader sells food grains at cost price but gives 10% less quantity to his customer. What is the percentage profit?
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Solution
As cost price is equal to selling price
% profit = \(\frac{Goods\, Left}{Goods\, Sold}\) = 100
= \(\frac{10}{90}\) x 100
= 11.11%
By selling 18 chocolates, a vendor loses the selling price of two chocolates. What is his percentage loss?
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Solution
Let the cost price of 1 choclate be x
Selling price of 1 choclate be y
As the transaction results in a loss
Total cost price - Total selling price = Loss
18x-18y =2y
18x = 20y
9x = 10y
\(\frac{x}{y}=\frac{10}{9}\)
\(\frac{Cost\, Price - Selling\, Price}{Cost\, Price}\)
∴ Loss = \(\frac{10-9}{10}=\frac{1}{10}\) = 10%