Sunday, 28 July 2013

QUANS - 11

QUANS - 11
1.      
      A student divided a number by 2/3 instead of multiplying the same by 3/2. Calculate the percentage of error in his calculation.

(a)    0%                  (b)   25%               (c)   44.44%         (d)  125%
Let the number be x.     Then  the actual result should be      x * 3/2  =   3x/2.
Due to the mistake of the student the result arrived was   x / 2/3  =  3x/2.
Since both the results are same there is no error in percentage.
Ans:  (a) 
2.       A man bought a Horse and Cart. If he sells the horse at 10% loss and the cart at 20% profit he will not lose anything. If he sells the horse at 5% loss and the cart at 5% gain then he will lose Rs 10 in the bargain. Find the amount paid by him for the purchase of the horse and the cart?

Let the price of the horse be H and that of the cart C.
Then we have an equation:   H + C = 0.9H + 1.2C (Horse was sold for 10% loss and Cart 20% profit)    Solving the two we get   0.2C – 0.1H = 0 -----------(i)

0.95H + 1.05C = H + C – 10  (Horse was sold for 5% loss and Cart for 5% profit)
Solving the above we get  0.05C – 0.05H = -10--------------(ii)
Equating (i) and (ii)                         0.2C – 0.1H = 0
                                                                 0.05C – 0.05H = -10   we get 
Ans:    H = Rs 400.00 and C =Rs  200.00

3.       During a vacation time I had visited my cousin’s home town and had a wonderful time. We would go for jogging in the mornings and on some days instead played Tennis in the afternoons. There were days when we were too lazy to do anything and as such stayed at home. There were 14 days when we either went for jogging or played Tennis. There were 12 mornings and 18 evenings when we did nothing or stayed at home. How many days did I stay at my cousin’s place?

Let A, B and C represent the days when we went for jogging, or played Tennis or stayed at home. We now have the following information.

B + C = 12,     A + C = 18, and  A + B = 14    Adding all the three, we get
2( A+B+C) = 44     A + B + C = 22

A = 22 – 12  =  10,           B = 22 – 18 = 4,       C =  22 – 14 = 8

Thus I stayed for 22 days at my cousin’s place.

4.       A stamp collector has the habit of arranging and re-arranging his stamps now and then. In one such case when he arranged the stamps in pairs one stamp was left out. When arranged in groups of three, four, five and six in each case one stamp remained. However, when arranged in group of seven thre was no stamp remaining. How many stamps he had with him?

The number should be an unknown figure say ‘x’ and the number of stamps is arrived at

X (LCM of 2,3,4,5,and 6) + 1                 x * 60 + 1  =    60x + 1.
Now substituting value for ‘x’ from 1 onwards we observe that 5 fits in nicely. Applying the value of 5 for ‘x’
The total number of stamps comes to 5*60+1 = 301 which is divisible by 7 without any reminder and fulfils the oter conditions in the question. Hence,
Ans: 301

5.       A truck when travelling at a speed of 30 km/hr  reaches the destination one hour earlier and when travels at 20 km/hr is late by one hour. At what speed the truck should go to reach the place on time?

Distance / speed = time       Let D be the distance travelled by the truck. Then we have an equation             D/20 – D/30 = 2 .     Solving, we get the distance as 120 km.
At a speed of 30 km/hr the truck will take 120/30 = 4 hours and is one hour early.
Hence the actual time to travel should be 5 hours and applying this, we get the speed as
120 / 5 = 24 km/hr.
Ans:  24 km/hr.

6.       A lady visits a restaurant and after having her food, pays half the amount she had towards the bill plus $1 as tip. She then visits the nearby mall and purchases some articles and pays half the amount she is left towards cost of purchases and on coming outside saw a beggar and gave him $2. Finally she visits the nearby bookshop purchased some books and paid half the money she is left with and after coming out saw another beggar and gave him $3. She was now left with $1 only. How much money she had originally?

This question is best Answered going from backwards.
She was left with $1 and prior to that had given the beggar $3. Totalling it comes to $4 which represents half the money after her paying for the books. Hence, while entering the book shop she was having  $4 * 2 = $8
Earlier to this while leaving the mall she was having this much of money with her and prior to that had given another beggar $2. Totalling these two amounts comes to $10 which incidentally is half the amount left with her after paying for the goods at the mall.
Hence, before entering the mall she was having $10 * 2 = $20 with her.
This was the sum she was having while leaving the restaurant where she gave a tip of $1. Together the sum works out to $ 21 which again was half the amount she had originally.
Hence the amount she had originally was $21 * 2 = $ 42.
Ans: $42
7.       A tree on the first day grows half its height, on the second day the tree grows 1/3 of its height the previous day, on the third day ¼ th of the height on the second day, on the fourth day 1/5th of the height on the third day and so on.  Find on which day the tree will be 100 times its original height?

Let the initial height of the tree be ‘x’
On the first day the height of the tree will be  x * ½ = 3/2 x
On the second day the height will be  3/2 *1/3 = ½ + 3/2 = 2x
On the 3rd day the height will be 2 * ¼ = ½ + 2x = 5/2 x and so on.
In other words the tree grows at the rate of ½ its original height every day.
Every two days the tree grows its original height of ‘x’. Going on this basis, we observe
The tree will be 100 times its original height on the 198th day.
Ans: 198 days.

8.       The length of the side of a square is (x+2) and the side of an equilateral triangle is 2x. If the perimeter of the Triangle and the Square are equal, then what is the value of ‘ x ‘?

We have the following equation from the given information.
2x * 3 = 4(x+2)     6x = 4x + 8    2x = 8      x = 4
Ans: x = 4.

9.       Find the next term in the series:   6, 24, 60, 120, 210, ?

The series goes in this format : 1*2*3=6,   2*3*4=24,   3*4*5=60,     4*5*6=120,  etc
The next series is 6*7*8=336
Ans: 336

10.   Find the next term in the series:  1, 5, 13, 25, ?
The series follows the pattern (n-1)2 + n2  Hence the answer is (5-1)2 + 52 = 41.
Ans: 41
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