QUANT QUIZ

1.A path of uniform width surrounds a circular park. The difference of internal and external circumferences of this circular path is 132 metres. Its width is: (Take π=22/7)  

A.22m

B.20 m

C.21m

D.24m

2.A train 800 metre long is running at the speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in metres) is :

A.77200

B.500

C.1300

D.13

3.A man rows a boat 18 kilometres in 4 hours downstream and returns upstream in 12 hours. The speed of the stream (in km per hour) is:

A.1

B.1.5

C.2

D.1. 75

4.8% of the voters in an election did not cast their votes. In this election, there were only two candidates. The winner by obtaining 48% of the total votes defeated his contestant by 1100 votes. The total number of voters in the election was:

A.21000

B.23500

C.22000

D.27500

5.A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they next meet at the starting point again?

A.46 minutes 12 seconds

B.45 minutes 12 seconds

C.42 minutes 36 seconds

D.26 minutes 18 seconds

6.A trader marks his goods at 20% above the cost price. If he allows a discount of 5% on the marked price, what profit per cent does he make?

A.14%

B.16%

C.18%

D.20%

7.8 men can do a work in 12 days. After 6 days of work, 4 more men were engaged to finish the work. In how many days would the remaining work be completed?

A.2

B.3

C.4

D.5

8.In an alloy, the ratio of copper and zinc is 5 : 2. If 1.250 kg of zinc is mixed in 17 kg 500 g of alloy, then the ratio of copper and zinc will be

A.2 : 1

B.2 : 3

C.3 : 2

D.1 : 2

9.The simple interest on a certain sum for 8 months at 4% per annum is Rs. 129 less than the simple interest on the same sum for 15 months at 5% per annum. The sum is :

A.Rs. 2,580

B.Rs. 2400

C.Rs. 2,529

D.Rs. 3600

10.40 liters of a mixture of milk and water contains 10% of water, the water to be added, to make the water content 20% in the new mixture is :  

A.6 litres

B.6. 5 litres

C.5.5 litres

D.5 litres

ANSWERS AND SOLUTION:

1. (3)  Let the internal radius of the park be r and the external radius (with the path) be R. 

The difference between the internal and external circumferences is 132m. 

so  2πR-2πr = 132 

 =>2π(R-r)  = 132

=R – r = 132/2π 

= (132 * 7)/(2 * 22) = 21 

Hence, the width of path 

= 21 metres 

2.(2) 

3.(1) Rate downstream 

= 18/4 = 9/2 kmph 

Rate upstream = 18/12 = 3/2 kmph. 

Now, speed of the stream 

= (Rate downstream – Rate upstream)/2 

=((9/2)-(3/2))/2=6/4 =3/2 =1.5kmph

  

4.(4) Let the total number of votes be 100. 

Number of uncast votes = 8 

so Number of votes obtained by the winner = 48 

Number of votes obtained by the loser = 48 – 44 = 4 

If the difference of win be 4 votes, total voters = 100 

so When the difference be 1100 votes, total voters 

= 100/4 * 1100 = 27500

5.(1) Required time = LCM of 252. 

308 and 198 seconds. 

Now, 252 = 2 * 2* 3 * 3 * 7 

308 = 2 * 2 * 7 * 11 

198 = 2 * 3 * 3 * 11 

so LCM = 2 * 2* 3 * 3 * 7 * 11 

= 36 * 77 seconds 

= (36 * 77)/60 minutes 

= 231/5 = 46 minutes 12 seconds

6.(1) Let the cost price = Rs. x 

Marked price = x + 20% of x 

= x + x/5 = Rs. 6x/5 

Selling Price 

= Rs. (6x/5 – 5% of 6x/5) 

= Rs. 6x/5 (1 – 1/20) 

= Rs. 6x * 19/20 

= Rs. 57x/50 

Profit = 57x/50 – x = Rs. 7x/50 

Profit% 7x/50/x * 100 = 14% 

7.(3) Work done by 8 men in 6 days 

= 6/12 = 1/2

Remaining work = 1 –1/2 = 1/2

4 more men are engaged. 

Total number of men 

= 8 + 4 = 12 

By work and time formula 

W1/M1D1= W2/M2D2, we have 

1/8*12 = ½/(12 * D2)

= D2 = ½ * 8 * 12/12 

= 4 days

  

8.(1) Weight of copper in 17 kg 500 gm i.e. 17500 gm of alloy

= 5/7 * 17500 = 12500 gm 

Weight of zinc = (17500 – 12500)

= 5000 gm 

1250 gm of zinc is mixed in alloy. 

Total weight of zinc 

= 1250 + 5000 = 6250 gm. 

Required ratio 

= 12500 : 6250 = 2 : 1 

9.(4) Let the sum be Rs. x 

(x * 5 * 15)/(100 * 12) – (x * 4 * 8)/(100 * 12) = 129 

= x/(100 * 12) (75 - 32) = 129 

X = (129 * 1200)/ 43 

Rs.   3600 

10.(4) Water content in 40 litres of mixture = 40 * 10/100 

4 litres. 

so Milk content = 40 – 4 

36 litres 

Let x litres of water is mixed. 

(4 + x)/(40 + x) = 20/100 

(4 + x)/ (40 + x) = 1/5 

=20 + 5x = 40 + x 

4x = 20 

X = 5 litres