**1. Peter wants to attend the drama performance of Mary Jane in the theatre near Peter's home. The theatre is at a distance of 6 km from his home and he travels at a constant speed. He travelled half the way with the specified speed and stopped for 5 minutes to buy flowers. To reach the theatre on time, he had to increase his speed by 6 km/hr for the rest of the way. Next week, he again went to see the drama, but this time he stopped for 10 minutes to buy flowers. By what value must he increase his speed for the remaining half of the distance to reach the theatre as per the schedule?**

A) 24kmph

B) 8 kmph

C) 6 kmph

D) 12 kmph

E) Can’t be determined

**2. Gary and Harry have some amount of money in the form of Rs. 2 and Rs. 5 coins. The average amount of money Gary and Harry have in form of Rs. 2 coins is Rs. 15, while that in form of Rs. 5 coins is Rs. 50. What is the number of Rs. 2 coins that Gary has if Gary and Harry have money in the ratio 8 : 5?**

A) 15

B) 10

C) 5

D) 0

E) Can’t be determined

**3. Nathan is a middleman. He buys chairs from factory and sells to public with profit. The difference between the prices at which he bought and at which he sold a chair is Rs. 20. If Nathan had sold at 10% more price, he would have made a profit of 21.58%. Find the price at which Nathan bought a chair from factory.**

A) Rs.180

B) Rs.190

C) Rs.200

D) Rs.210

E) Rs.240

**4. A sample of 20 litres air is taken in which there are no impurities. It has 78% Nitrogen and 22% Oxygen. In this mixture, some pure oxygen is mixed so that the amount of oxygen and nitrogen becomes equal. How much more pure oxygen should be added so that ratio of Nitrogen and Oxygen becomes 1:4?**

A) 25.2 litres

B) 29.8 litres

C) 38.7 litres

D) 41.2 litres

E) 46.8 litres

**5. If 25 students can paint a wall in 2 hours. But at the end of every 10 mins, 10 additional students join. In how much time will the whole wall be painted?**

A) 40 mins

B) 50 mins

C) 53 mins

D) 60 mins

E) 55 mins

**6. The length, breadth and height of an open box is 60 cm, 50 cm and 30 cm respectively. Its thickness is 5 cm. What would be the cost of the box if 1 cm**

^{3}of wood costs Rs. 0.08?
A) Rs.3740

B) Rs.3800

C) Rs.3860

D) Rs.3200

E) Rs.3840

**7. Every day, Bobby eats three chocolates while Gary eats five candies. The price of seven candies and two chocolates is Rs. 69. Also, price of three chocolates is Rs. 16 more than the price of two candies. How much do Bobby and Gary spend together every day on chocolates and candies?**

A) Rs.17

B) Rs.51

C) Rs.65

D) Rs.34

E) Rs.9

**8. Jack owned 950 gold coins all of which he distributed amongst his three Friends John, James and Nick. John gave 25 gold coins to his wife. James donated 15 gold coins and Nick made jewellery out of 30 gold coins. The new respective ratio of the coins left with them was 20 : 73 : 83. How many gold coins did James receive from Jack?**

A) 380

B) 415

C) 400

D) 350

E) None of these

**9. Harry is an elite customer of a bank, while Gary is a normal customer. Bank gives a simple interest of 5% to Harry and 4% to Gary. So, instead of investing in Bank, Gary gave his sum of money of Rs. 34000 to Harry so that he can invest on his behalf for a year. Harry promised a 4.5% interest rate to Gary. Harry also invested Rs. 19000. Harry returned Gary’s money along with promised interest at the end of year. How much money Harry has at the end of year?**

A) Rs.2000

B) Rs.19860

C) Rs.20100

D) Rs.20120

E) Rs.20480

**10. Stacy and James entered into a partnership and invested equal sums of for a year. The profit that this investment offers is 15% for a year. Due to a financial constraint, James withdrew his share after 7 months. As a clause of partnership, James only received back his original sum and his earned profit went to Stacy. In total, Stacy earned a profit of Rs. 1543.75. How much money each of them invested?**

A) Rs.5500

B) Rs.6000

C) Rs.6500

D) Rs.7200

E) Rs.7500

**Solutions:**

**1. A)**Let the regular speed of the Peter = x km/hr.

Now, time =
distance/speed

∴ regular time taken by Peter to travel the full distance =
(6/x) hrs

**Case-1:**

Distance travelled at
regular speed = 6/2= 3 km

∴ time taken to travel this distance = (3/x) hrs ---(1)

Waiting time = 5 mins =
1/12 hrs

⇒ for the remaining 3 kms, the man increases his speed by 6
km/h (i.e. x + 6)

∴ time taken to travel last 3 km = 3/(x + 6) ---(2)

From the given data, we
can clearly deduce that:

Regular time = (time
taken to travel first 3 km) + (waiting time) + (time taken to travel last 3 km)

=> 6/x = 3/x + 1/12 +
3/(x + 6) => 3/x – 3/(x + 6) = 1/12 => 1/(x2 + 6x) = 1/216 => ⇒ x

^{2}+ 6x – 216 = 0 ⇒ (x + 18) (x - 12) = 0
Omitting the negative
value of speed,

x = 12 km/h

Now, in the second case:

Peter travels first 3 kms
at its regular speed and waits for 10 mins.

In this case: waiting
time = 1/6 hrs

Let y = the speed with
which he travels the remaining distance.

Again, he reaches the
destination in regular time.

=> 6/x = 3/x + 1/6 +
3/y => 3/x= 1/6 + 3/y

Substituting x = 12,

⇒ y = 36 km/h

Increase in usual speed =
y – x = 36 – 12 = 24 km/hr

**2. E)**The average amount of money Gary and Harry have in form of Rs. 2 coins is Rs. 15, while that in form of Rs. 5 coins is Rs. 50.

⇒ Total coins of Rs. 2 = (15 × 2)/2 = 15

⇒ Total coins of Rs. 5 = (50 × 2)/5 = 20

Suppose Gary has M coins
of Rs. 2, and N coins of Rs. 5.

=> {2M + 5N}/{[2(15 –
M) + 5(20 – N)]}

⇒ 10M + 25N = 240 – 16M + 800 – 40N

⇒ 26M + 65N = 1040

⇒ 2M + 5N = 80

⇒ M = 40 – 2.5N

We know, M and N must be
greater than or equal to 0. M should be less than equal to 15, and N should be
less than equal to 20.

In this equation, for M
to be integer, N must be even.

For M to be less than 15,
N should be at least 10.

Following pairs of M and
N will satisfy given conditions, (15, 10), (10, 12), (5, 14), (0, 16).

Hence, number of Rs. 2
coins with Gary cannot be uniquely determined.

**3. B)**Suppose Nathan bought a chair from factory at Rs. T.

Price at which Nathan
sold chair to Public = Rs. (T + 20)

If Nathan had sold at 10%
more price, he would have made a profit of 21.58%.

In this case, selling
price would become Rs. (T + 20) × (1 + 10/100) = Rs. (1.1T + 22)

We know, Selling Price =
Cost price × (1 + (Profit Percentage)/100)

⇒ 1.1T + 22 = T × (1 + 21.58/100)

⇒ 1.1T + 22 = 1.2158T

⇒ T = 22/0.1158 = 190

∴ Price at which Nathan bought chair from factory is Rs. 190.

**4. E)**Amount of Nitrogen in 20 litres air = (20 × (78/100)) = 15.6 litres

Amount of Oxygen in 20
litres air = (20 × (22/100)) = 4.4 litres

To make oxygen and
nitrogen equal, amount of oxygen to be added will be (15.6 – 4.4) litres, i.e.,
11.2 litres.

Total amount of air now =
20 litres + 11.2 litres = 31.2 litres

And it has 15.5 litres of
each of nitrogen and oxygen.

Suppose T litres of
oxygen are added to mixture, so that ratio of Nitrogen and Oxygen becomes 1:4.

⇒ 15.6/(15.6 + T) = ¼

⇒ 62.4 = 15.6 + T

⇒ T = 46.8

∴ 46.8 litres of oxygen should be added.

**5. D)**25 students can paint the wall in 2 hours = 2 × 60 = 120 min.

⇒ part of wall painted by 25 students in one minute = 1/120

⇒ part of wall painted by 1 student in 1 min = 1/(120 × 25)

For the 1

^{st}10 min, there are only 25 students
⇒ part of wall painted by 25 students in 10 min can paint =
(25 × 10)/(120 × 25) = 1/12

∴ Total part of the wall painted after 10 min = 1/12

**6. D)**The outer dimensions of the box are as follows:

Length = l

_{1}= 60 cm; Breadth = b_{1}= 50 cm; Height = h_{1}= 30 cm
Now, since the box is
wooden and has a thickness of 5 cm, only the edges would be made of wood and
there’ll be cavity inside the box. The dimensions of the cavity would be as
shown in the figure.

Length = l

_{2}= 50 cm; Breadth = B_{2}= 40 cm; Height = H_{2}= 25 cm
Now, Volume of wood used
for box = volume of box – volume of cavity

⇒volume of wood used for the box = (l

_{1}× b_{1}× h_{1}) – (l_{2}× b_{2}× h_{2})
⇒volume of wood used for the box = (60 × 50 × 30) – (50 × 40 × 25)

⇒volume of wood used for the box = 90000 – 50000 = 40000 cm

^{3}
∴ Cost of wood = rate of wood × volume of wood

⇒ Cost of wood = 0.08 × 40000 = Rs. 3200

**7. C)**Let price of chocolate is M rupees and price of candy is N rupees

Price of 7 candies and
two chocolates is Rs. 69

⇒7N + 2M = 69 -------- (i)

Difference between
prices of three chocolates and two candies is Rs. 16.

3M – 2N = 16 --------
(ii)

Let us solve (i) and
(ii), multiply (i) by 2 and (ii) by 7, and then add

2(7N + 2M) + 7(3M – 2N) =
2 × 69 + 7 × 16

⇒ 25M = 250

⇒ M = 10

Substitute this value in
equation (ii)

3 × 10 – 2N = 16

⇒ 2N = 14

⇒ N = 7

Price of one chocolate =
Rs. 10

Price of one candy = Rs.
7

Bobby eats three
chocolates and Gary eats five candies, everyday.

⇒ Money Spent every day = Rs (3 × 10 + 5 × 7) = Rs. 65

**8. A)**Jack have total gold coins = 950

No. of total gold coins
left after donating to three friends = 950 – (25 + 15 + 30) = 880

According to question,
the new respective ratio of the coins left with them was 20 : 73 : 83

Let us consider coins
left with them are 20k, 73k and 83k respectively.

⇒ 20k + 73k + 83k = 176k

Now, in order to find the
ratio of coins for one part

⇒ k = 880/176 = 5

So, James’s coins = 73 ×
5 = 365

James has donated 15
coins.

So, Total coins that
James received = 365 + 15 = 380 coins

∴ James got 380 from his friend Jack.

**9. D)**Bank gives a simple interest of 5% to Harry and 4% to Gary.

Gary gave his sum of
money of Rs. 34000 to Harry so that he can invest on his behalf for a
year. Harry promised a 4.5% interest rate to Gary, but got an interest of
5% from bank. So, Harry got 0.5% profit on Gary’s investment.

Harry also invested
Rs. 19000. On this, he will get 5% interest.

We know, Simple interest
= (Principal × Rate × Time)/100

⇒ Total interest earned by Harry = (34000 × 0.5 × 1)/100 + (19000 × 5 × 1)/100 = 1120

∴ Total amount of money that Harry will have at end of year =
Money Harry initially had + Interest earned = Rs. 19000 + Rs. 1120 = Rs. 20120

**10. C)**Suppose both Stacy and James invested Rs. T each.

Profit earned by James in
7 months = T × (15/100) × (7/12) = 0.0875T

As a clause of
partnership, James only received back his original sum and his earned profit
went to Stacy.

Profit earned by in Stacy
12 months = T × (15/100) × 1 = 0.15T

In total, Stacy earned a
profit of Rs. 1543.75.

⇒ 0.0875T + 0.15T = 1543.75

⇒ T = 1543.75/0.2375 = 6500

∴Each of them invested an amount of Rs. 6500.