A series of books were published at seven years intervals when the seventh book was issued the sum of the publications years was 13524, when the first book was published?
x+x+7+x+14+x+21+x+28+x+35+x+42=13524
7x+147=13524 then x=1911
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In the town of Unevenville, it is a tradition to have the size of the front wheels of every cart different from that of the rear wheels. They also have special units to measure cart wheels which is called uneve. The circumference of the front wheel of a cart is 133 uneves and that of the back wheel is 190 uneves. What is the distance traveled by the cart in uneves, when the front wheel has done nine more revolutions than the rear wheel?
So, to cover this distance, front wheel takes 10 rounds, and back wheel takes 7 rounds.
So, for 3 rounds extra, 1330 uneves distance has to be travelled.
To take 9 rounds extra, 1330 * 3 = 3990 uneves has to be traveled.
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Water is continuously poured from a reservoir to a locality at the steady rate of 10,000 liters per hour. When delivery exceeds demand the excess water is stored in a tank. If the demand for 8 consecutive three-hour periods is 10000, 10000, 45000, 25000, 40000, 15000, 60000 and 35000 liters respectively, what will be the minimum capacity required of the water tank (in 1000 liters) to meet the demand?
In the period of first 3 hrs, the demand of water = 10000.
But the water poured is 10000 per hour.
Thus at the end of 3 hours, it will pour 30000 ltr, then the excess of water = 20000.
Similarly at the end of 2nd 3 hr period the excess of water 20000+20000 = 40000.
Third, 3 hrs water poured = 30000
already we have 40000 of excess water and demand 45000.
Then the excess water at the end of 3rd 3 hrs
= 40000+30000-45000
= 25000
Fourth 3 hrs. water = 25000+30000â€“25000
= 30000
Fifth = 30000+30000â€“40000
= 20000
Sixth = 20000+30000â€“15000=35000
Seventh = 35000+30000â€“60000
= 5000
Eighth = 5000+30000â€“35000
= 0
By analyzing the above results, we have 40000 ltrs is the highest measure of excess water.
So the minimum capacity of water tank = 40000 litres = 40
i.e. = 40
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Three wheels make 18, 24, 54 revolutions per minute. Each has a black mark on it. It is aligned at the start. When does it align again for the first time?
Let the numbers be 12a,12b where gcd(a,b)=1. (By the definition of HCF).
Also, 12b−12a=12.
⟹b−a=1
So, we are left with two equations,
gcd(a,b)=1 and
b−a=1
Which is true for all adjacent pairs of natural numbers. Therefore,
(a,b)=(1,2)(2,3),(3,4),(4,5),…
Which means,
(12a,12b)=(12,24),(24,36),(36,48),(48,60),(84,96)…
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HCF of \(2^2 \times 3^2 \times 7^2\) and \( 2 \times 3^4 \times 7\) is?
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