Directions(Q.1-5): In a recently held survey there were 7500 persons in an area. Out of those, 2500 opted for company X’s mango juice, 1850 opted for company Y’s mango juice and 950 opted only for company Z’s mango juice. The number of persons opting for all the companies is 1000. The number of persons opting for Company X and company Z is 250. The number of people opting only for Company Y and Z is 200 and the number of people opting only for company X and Y is 150.

1. How many persons opted for at least two companies

(a)800

(b)1000

(c)1600

(d)1850

2. Number of people who opted for company X’s mango juice is?

(a)3900

(b)3500

(c)2500

(d)1450

(e)none of these

3. How many people have opted for only one company’s mango juice?

(a)4725

(b)5000

(c)5300

(d)5500

(e)none of these

4. How many persons did not participate in the survey?

(a)600

(b)800

(c)900

(d)1000

(e)none of these

5. The number of persons opting only for company X’s mango juice Is what percent of total number of person’s opting for only company Y’s and company Z’s mango juice?

(a)92%

(b)85%

(c)89.28%

(d)84.14%

(e)none of these

6. Narmada is standing on a railway bridge which is 180 m long. She finds that a train crosses the bridge in 20 seconds but herself in 8 seconds. Find the speed of the train?

(a)31kmph

(a)31kmph

(b)54kmph

(c)46kmph

(d)37kmph

(e)40kmph

7. Sujoy Chakarborty undertakes to supply 2000 pieces of a particular component at Rs.25 per piece. According to his estimates, even if 5% fail to pass the quality tests, then he will make a profit of 25%. However as it turned out, 50% of the components were rejected. What is the loss to the Sujoy?

(a)11000/-

(b)11500/-

(c)12000/-

(d)12500/-

(e)13000/-

8. Gaurav invested certain amount in three different schemes P, Q and R with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in Scheme R was 150% of the amount invested in Scheme P and 240% of the amount invested in Scheme Q, what was the amount invested in Scheme Q?

(a)10,000/-

(b)7500/-

(c)50000/-

(d)5000/-

(e)7590/-

9. The sum of ages of family members (both children and parents) is 360 years. The total ages of children and parents are in the ratio 2:1 and the ages of wife and husband are in the ratio 5:7.What will be the age of husband?

(a)70years

(b)72years

(c)68years

(d)66years

(e)none of these

10. The average price of 10 books is Rs. 12 while the average price of 8 of these books is Rs. 11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what is the price of each of these two books?

(a)Rs.16 and Rs.20

(b)Rs.22 and Rs.14

(c)Rs.12 and Rs.22

(d)Rs.10 and Rs.20

(e)Rs.10 and Rs.16

Answers:

1.c

2.a

3.c

4.a

5.c

6.b

Let the length of the train be x metres.

Then, the train covers x metres in 8 seconds (train is actually covering itself because length of man is very less comparable to train)and (x + 180) metres in 20 seconds.

equate speed in both cases=d/t∴ x/8 =( x + 180) / 20 ⇔ 20x = 8(x + 180) ⇔ x = 120.

∴ Length of the train = 120 m.

Speed of the train = [120/8]m/sec (convert to km/hr. i.e. x 18/5)

=[120/8] x 18/5kmph = 54 kmph

Then, the train covers x metres in 8 seconds (train is actually covering itself because length of man is very less comparable to train)and (x + 180) metres in 20 seconds.

equate speed in both cases=d/t∴ x/8 =( x + 180) / 20 ⇔ 20x = 8(x + 180) ⇔ x = 120.

∴ Length of the train = 120 m.

Speed of the train = [120/8]m/sec (convert to km/hr. i.e. x 18/5)

=[120/8] x 18/5kmph = 54 kmph

7.e

5% of 2000=100 so 2000-100=1900

so, if he sells 1900 he will get 25% profit

cost per piece Rs 25……so 25x 1900

if 125%…………………..25×1900

100 %………………….?

?= 25x1900x100/125=38000=CP

if 50% rejected, only 1000 pieces sold

so 1000×25=25000=SP

loss=cp-sp= 38000-25000=13000

cost per piece Rs 25……so 25x 1900

if 125%…………………..25×1900

100 %………………….?

?= 25x1900x100/125=38000=CP

if 50% rejected, only 1000 pieces sold

so 1000×25=25000=SP

loss=cp-sp= 38000-25000=13000

8.d

Let x, y and z be the amounts invested in schemes P, Q and R respectively.

Then,

add individual interest to get total using SI= p*r*t/100

[x * 10 * 1]/100 + [y x 12 x 1]/100 + [z x 15 x 1]/100 = 3200

10x + 12y + 15z = 320000…………..1

add individual interest to get total using SI= p*r*t/100

[x * 10 * 1]/100 + [y x 12 x 1]/100 + [z x 15 x 1]/100 = 3200

10x + 12y + 15z = 320000…………..1

Now, z = 240% of y =(12/5)y……… 2

And, z = 150% of x =(3/2)x so, x=(2/3 )z = (2/3) x value of z from 2

x= (2/3) x (12/5) y = (8/5)y………..3

From (1), (2) and (3), we have :

16y + 12y + 36y = 320000

y = 5000

x= (2/3) x (12/5) y = (8/5)y………..3

From (1), (2) and (3), we have :

16y + 12y + 36y = 320000

y = 5000

9.a

sum of ages is 360 years.

The ratio of children and parents ages is 2:1.

Total age of parents = 360 x 1 / 3 = 120 years

Ratio of wife and husband age is 5:7.

Total age of parents = 360 x 1 / 3 = 120 years

Ratio of wife and husband age is 5:7.

Therefore, the age of husband = 120 x 7 / 12 = 70

10.e

Total price of the two books = Rs. [(12 x 10) – (11.75 x 8)] = Rs. (120 – 94) = Rs. 26

Let the price of one book be Rs.x

Then, the price of other book = Rs. (x + 60% of x )= x + (3/5)x= (8/5)x

so, x +(8/5)x=26 , x=10

The prices of the two books hence are Rs. 10 and Rs. 16

Let the price of one book be Rs.x

Then, the price of other book = Rs. (x + 60% of x )= x + (3/5)x= (8/5)x

so, x +(8/5)x=26 , x=10

The prices of the two books hence are Rs. 10 and Rs. 16