Maths Quiz 22/12/2015

#EVERYDAYQUIZ  10Q

1.There are 6 boxes numbered 1,2,...6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is:

A.5

B.21

C.33

D.60

E.27

2.The least perfect square, which is divisible by each of 21, 36 and 66 is?

A.213414

B.213424

C.213434

D.213444

E.none of these

3.Average of 10 numbers is zero. At most how many numbers may be greater than zero?

A.0

B.1

C.5

D.9

E.none of these

4.Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40 and 60 km per hour respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?

A.3

B.3.5

C.4

D.4.5

E.none of these

5.A work is done by three person A,B and C. A alone takes 10 hours to complete a single product but B and C working together takes 4 hours, for the completion of the same product. If all of them worked together and completed 14 products, then how many hours have they worked?

A.20 hrs

B.28 hrs

C.40 hrs

D.54 hrs

E.none of these

6.In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

A.70%

B.80%

C.90%

D.85%

E.None of above

7.A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 21 per kg, then his gain percent is?

A.12%

B.13%

C.14%

D.15%

E.None of above

8.In a mixture 60 litres, the ratio of milk and water 2 : 1. If the this ratio is to be 1 : 2, then the quanity of water to be further added is?

A.20 liters

B.30 liters

C.50 liters

D.60 liters

E.None of above

9.Rs. 800 becomes Rs. 956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what amount will Rs. 800 become in 3 years?

A.Rs 1052

B.Rs 1152

C.Rs 1252

D.Rs 1352

E.None of above

10.A bus without stopping travels at an average speed of 60 km/hr and with stoppages at an average speed of 40 km/hr. What is the total time taken by the bus for stoppages on a route of length 300km?

A.4 hr

B.3 hr

C.2.5 hr

D.3.5 hr

E.None of above

Answers:

1.B
2.D
3.D
4.C
5.C
6.A
Let C.P.= Rs. 100.
Then, Profit = Rs. 320,
S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295
Required percentage = (295/420) * 100
= 70%(approx)

7.A
Suppose he bought 5 kg and 3 kg of tea.
Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150.
Selling price = Rs. (8 x 21) = Rs. 168.
Profit = 168 - 150 = 18
So, Profit % = (18/150) * 100 = 12%

8.D
Quantity of Milk = 60*(2/3) = 40 liters
Quantity of water = 60-40 = 20 liters
As per question we need to add water to get quantity 2:1
 40/(20+x) = 1/2
 20 + x = 80
 x = 60 liters

9.A
10.C

Ques 1:
If one green box, then there are = 6 ways
If two green boxes, then to be consecutive (12, 23, 34, 45, 56), there are = 5 ways
If three green boxes, (123, 234, 345, 456), then there are = 4 ways.
Similarly 3, 2, 1 ways for four, five, six green boxes.
Total = 6+5+4+3+2+1 = 21 ways

Ques 2:
21 = 7*3; 36 = 9*4; 66 = 11*6
So, we're looking for 7^2 * 2^2 * 3^2 * 11^2 = 213444

Ques 3:
Nine numbers could be > 0
Tenth negative number would be = sum of these nine number.

Ques 4:
Arun covered 30*2 = 60 km in 2 hours.
Relative speed of Barun with respect to Arun = 40-30 = 10 kmph.
Barun will cover this 60 km gap and catch Arun in 60/10 = 6 Hours.
In 6+2 = 8 Hours, Arun has covered = 30*8 = 240 km
Kiranmala could cover this 240 km in 240/60 = 4 Hours
So, only after 4 hours of Arun did Kiranmala started to travel.

Ques 5:
LCM(10,4) = 20. Let 20 units of work per product is there.
A does 20/10 = 2 units of work per hour
B+C does 20/4 = 5 units of work per hour
A+B+C does 7 units of work per hour
14 products = 14*20 units of work
All this work is done with speed of 7 units per hour in = 14*20/7 = 40 Hours.

Ques 9:
956-800 = 156; 156/3 = 52. Hence 52 Rs interest in 1 year
==> Rate of interest be 52*100/800 = 6.5%
6.5+4 = 10.5%
Interest in 3 year @10.5% = 800*10.5*3/100 = 252 Rs
Amount after 3 years = 800+252 = 1052 Rs

Ques 10:
With 60 kmph, he can travel 60 km in one hour
But with stoppages he travelled only 40 km
40 km could be travelled with speed of 60 kmph in 40/60*60 = 40 minutes
Hence, 60-40 = 20 minutes per hour = stoppage time
With 40 kmph, 300 km is travelled in 300/40 = 7.5 hours
In 7.5 hours journey, stoppage time is = 7.5*20 = 150 minutes = 2.5 hours.

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