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Directions : Study the following questions carefully and choose the right answer.
1
A packaging machine A of Kurkure can pack one lakh packets in 10 hours, packaging machine B of Kurkure can pack the same number of packets in 12 hours while packaging machine C can pack them in 15 hours. All the packaging machines are started at 8 a.m. while packaging machine A is closed at 10 a.m. And the remaining two packaging machines complete the work. Approximately at what time will the work be finished?
» Explain it
A
Packaging machine (A, B and C) together work in 1 hours
1  +  1  +  1  =  1
10 12 15 4

Work done by packaging machine (A, B and C) in 2 hours = 2 ×  1  =  1
4 2

Remaining work = 1 –  1  =  1
2 2

Packaging machine (B and C) together work in 1 hours
1  +  1  =  3
12 15 20

Now,  3  work is done by packaging machine B and C in 1 hour.
20

So,  1  work will be done by packaging machine B and C in  20  ×  1
2 3 2

10  = 3 hours 20 minutes
3

Hence, the work will be finished 3 hour 20 minutes after 10 a.m. I.e 1:20 pm.

Therefore, option (A) is correct.
 
2
The New Delhi - Howrah Rajdhani express is running at 75 kmph takes 15 seconds to pass Dhanbad platform. Next it takes 9 sec to pass a man walking at 5 kmph in the same direction in which the New Delhi - Howrah Rajdhani express is going. Find the length of the New Delhi - Howrah Rajdhani express and the length of the Dhanbad platform.
» Explain it
A
Let the length of New Delhi – Howrah Rajdhani express be x meters and length of Dhanbad platform be y meters.

Speed of the the New Delhi – Howrah Rajdhani express relative to man= (75 – 5) kmph = 70 kmph

70 × 5  m/sec =  175  m/sec
18 9

In passing a man, the New Delhi - Howrah Rajdhani express cover it's own length with relative speed.

Length of the New Delhi – Howrah Rajdhani express = (Relative speed × Time)
175  × 9 = 175 meters.
9
Also, speed of the New Delhi – Howrah Rajdhani express
= 75 ×  5  =  125 m/s
18 6

Since,  x + y  = 15
125
  6  

x + y =  125 × 15  = 312.5
6

y = 312.5 – 175 = 137.5 meters

Hence, option (A) is correct.
 
3
In Kolkata consisting of three localities Salt Lake, South Kolkata and Rajarhat the population of the three localities Salt Lake, South Kolkata and Rajarhat are in the ratio 9 : 8 : 3. In Salt Lake, 80% of the people are literate, in South Kolkata, 30% of the people are illiterate. If 90% people in Rajarhat are literate. Find the percentage literacy in these three localities in Kolkata.
» Explain it
A
Let the population of Salt Lake = 9x, 
 
The population of South Kolkata = 8x, and 
 
The population of Rajarhat = 3x
 
The total population of these three localities = 9x + 8x + 3x = 20x
 
The number of literate in Salt Lake = 80% of 9x = 7.2x
 
The number of literate in South Kolkata = 70% of 8x = 5.6 x
 
The number of literate in Rajarhat = 90% of 3x = 2.7x
 
The total number of literate in these three localities = 7.2x + 5.6x + 2.7x = 15.5x

Hence. Required percentage =  15.5 x  × 100 = 77.5%
20x

Therefore, option (A) is correct.

4
Sohan purchased 35 bonds of three different companies Tata, Minda and Kelton Tech and the total cost was Rs. 69600. The prices of each of these bonds were Rs. 1200, Rs. 1800 and Rs. 2400 respectively. He purchased not less than 5 bonds of any company and he purchased an even number of bonds of the company Tata. What is the possible number of bonds of the company Tata and Kelton Tech did he purchase?
» Explain it
D
Let the number of bonds purchased of the companies Tata, Minda and Kelton Tech be p, q and r respectively.

Given that,

p + q + r = 35        ...…. (i)

Also, 1200p + 1800q + 2400r = 69600

2p + 3q + 4r = 116         ..….. (ii)

From (i) and (ii)

q + 2r = 46           …… (iii)

As we can see that, in equation (iii), 2r and 46 are even, so q must be also even

Given that p, q ≥ 5

Now,

Q 6 8 10 12 14
R (46 -6)/2 = 20 (46 - 8)/2 = 19 (46 - 10)/2 = 18 (46 - 12)/2 = 17 (46 - 14)/2 = 16
P 35 – (6 + 20) = 9 35 – (8 + 19) = 8 35 – (10 + 18) = 7 35 – (12 + 17) = 6 35 – (14 + 16) = 5

As p is even so, p = 8 and p = 6 are the only two possibilities.

If, p = 8 then r = 19

So, (p + r) = (8 + 19) = 27

If, p = 6 then r = 17

So, (p + r) = (6 + 17) = 23

Hence, the number of bonds purchased of the companies Tata and Kelton Tech together be either 23 or 27.

Hence, option D is correct.
5
Rampaal is a businessman and he goes on a business tour of three cities of Gujarat. In every city he spends Rs.30 more than one-third of the money he has with him. At the end of the tour, he has Rs.1000 left with him. What is the amount with him before he started the tour?
» Explain it
C
Let the amount with the Rampaal, before he started the tour of Gujarat be P

In the first city he spends =  P  + 30
3

He would be left with (P –  P  –  30) = [ ( 2P )  – 30]
3 3

At the end of the tour of the first city.

In the second city he spends  ( 1 )  ×  [ ( 2P )  – 30] + 30
3 3

2P  + 20
9

He would be left with [ ( 2P )  – 30] – [ ( 2P )  + 20]
3 9

4P  – 50 at the end of the tour of the second city.
9

In the third city he spends ( 1 ) ×  [ ( 4P )  – 50] + 30
3 9

4P  +  40
27 3

He would be left with [ ( 4P )  – 50] – [ ( 4P )  +  ( 40 ) ]
9 27 3

8P  –  190
27 3

Therefore, total amount left with him after the tour = Rs. 1000

⇒  8P  –  190  = 1000
27 3

⇒  8P  = 1000 +  190
27 3

⇒  8P  =  3190
27 3

⇒  8P  = 1063.33
27

⇒ P =  (1413.33 × 27)
8

⇒ P = 3588 (approx.)

Hence, the amount with  Rampaal, before he started the tour of Gujarat is Rs. 3588

Hence, option C is correct.