Question No.1 Question No.2 Question No.3 Question No.4 Question No.5 Question No.6 Question No.7 Question No.8 Question No.9 Question No.10 |
From 6
^{10} × 7^{17} × 55^{27}, we have to write each base in terms of multiplication of its prime factors.
That is,=(2X3) ^{10}×(7)^{17}×(5X11)^{27}
=2 ^{10}X3^{10}X7^{17}X5^{27}X11^{27}
The no. of prime factors = sum of the exponents = 10+10+17+27+27 = 91 Hence, the number of prime factors is 91.
When the two train running in opposite direction, relative speed = 60+48 = 108 kmph = 108X5/18 m/sec = 30 m/sec
Sum of the lengths of the two trains = sum of the distances covered by the two trains in the above relative speed Sum of the lengths of the two trains = 30X15 = 450 m When the two trains running in the same direction, relative speed = 60-48 =12 kmph = 12X5/18 = 10/3 m/sec When the two trains running in the same direction, a person in the faster train observes that he crossed the slower train in 36 seconds. The distance he covered in 36 seconds in the relative speed is equal to the length of the slower train. Length of the slower train = 36X10/3 = 120 m Length of the faster train = 450-120 = 330 m Hence, the length of the two trains are 330m and 120m
We can apply L.C.M method to solve this problem
Total work = 90 units (L.C.M of 15,30,18,9) (A+B) can complete 6 units/day (90/15 = 6) (B+C) can complete 3 units/day (90/30 = 3) (A+C) can complete 5 units/day (90/18 = 5) By adding, we get 2(A+B+C) = 14 units/day (A+B+C) = 14/2 = 7 units/day work done by A = (A+B+C)-(B+C)=7-3=4 units/day work done by B = (A+B+C)-(A+C)=7-5=2 units/day work done by C = (A+B+C)-(A+B)=7-6=1 unit/day work done by (A+B+C)in 9 days = 9X7 = 63 units. Balance work = 90-63 = 27 units This 27 units of work to be completed B & C. Because A left after 9 days of work. No. of days taken by B & C to complete the balance 27 units of work = 27/3 = 9 days. (Because B&C can complete 3 units of work per day)
Average speed = 2pq/(p+q), here p=25 q=4
= (2X25X4)/(25+4) Therefore, average speed = 200/29 km/hr And 5 hour 48 min = 5 ^{48}⁄_{60}hrs = 29/5 hours
Distance = Speed X Time Distance = (200/29)X(29/5) = 40 km Distance covered in 5 hrs 48 min = 40 km Hence,distance of the post office from the village = 40/2 = 20km
Let "x" be the present age of the son.Then the present age of father is (3x+3)
3 years hence, father's age will be 10 years more than twice the age of the son (3x+3)+3 = 2(x+3)+10 3x+6 = 2x+16 x = 10 To find the present age of the father, plug x = 10 in (3x+3) Present age of the father = 3(10)+3 = 33 years
If "x' be the first even number, then the four consecutive even numbers are x, x+2, x+4, x+6
Average of the four consecutive even numbers = 27 (x+x+2+x+4+x+6)/4 = 27 (4x+12) = 108 4x = 96 ===> x = 24 Hence the largest even number = x+6 = 30
From the given information, we have
Speed downstream = (14+4) = 18 kmph Speed upstream = (14-4) = 10 kmph Let "x" be the distance between A and B x/18 + (x/2)/10 =19 (Hint: Time = Distance/Speed) x/18 + x/20 =19 (10x + 9x)/180 = 19 (L.C.M of 18,20 is 180) 19x/180 = 19 x = 180 Hence the distance between A and B is 180 km.
Original weight of John = 56.7 kg (given)
He is going to reduce his weight in the ratio 7:6 [Hint:If a quantity increases or decreases in the ratio a:b, then new quantity = 'b' of the original quantity divided by 'a'] His new weight = (6x56.7)/7 = 6x8.1 = 48.6 kg.
Let the cost price of 1 ltr pure milk be $1
Now we take some quantity of milk (less than 1 ltr),add some water and make it to be 1 ltr mixture Let "x" be the money we invest for milk in 1 ltr of milk-water mixture Since the gain is 20%, selling price = x + 20%of x Selling price = 120% of x = (120/100)x = (6/5)x But the mixture is sold at the cost price of pure milk So, we have (6/5)x = 1 x = 5/6 Therefore cost price of the milk in the mixture = $(5/6 Cost price of the water = $0 Rule to find the ratio for producing mixture = (d-m):(m-c) (d-m):(m-c) = 1-5/6:5/6-0 = 1/6:5/6 = 1:5 So, water and milk to be mixed in the ratio to gain 20% is 1:5
Let A,B and C be the incomes of A,B and C respectively
From the given information, we have C = $1600 10% of B = 30% of C (10/100)B = (30/100)X1600 B = $ 4800 15% of A = 25% of B (15/100)A = (25/100)X4800 A = $8000 A+B+C = 8000+4800+1600 = 14400 Hence, the total income of A,B and C is $14400 |

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