**1. In a test, Kate has got 2 marks more than Stacy. If each of them gets 3 marks more, then twice the product of their marks will be 1350 more than the product of their actual marks. Minimum marks that can be obtained in test is 0. What is the sum of marks obtained by them?**

a) 54

b) 58

c) 62

d) 66

e) 74

**2. The area of a rectangle is twice the area of a parallelogram. The breadth of rectangle is half its length. The sum of lengths of two adjacent sides of parallelogram is 40 cm. Also, the perimeter of rectangle is 50% more than that of parallelogram. Find the area of parallelogram (in square cm).**

a) 300

b) 400

c) 440

d) 540

e) 720

**3. There are two tanks that are connected by a pipe. The rate of flow of water through this pipe is 20 litres per minute. The capacity of larger tank is twice the smaller tank. Initially, larger tank is 30% full and smaller tank is empty. After opening the pipe, it takes 40 minutes to reach a point where both tanks have equal amounts of water as a percentage of their total capacity. What is the capacity of the larger tank (in litres)?**

a) 6000

b) 7200

c) 8000

d) 8800

e) 9600

**4. Harry and Nick are running towards each other. The speed of Harry is twice the speed of Nick. To cover a distance of 42 km between them, they take 2 hours and 30 minutes. How much time will Harry take to chase Nick if they start running in same direction and with initial distance between them being 30 km?**

a) 5.12 hours

b) 5.36 hours

c) 5.5 hours

d) 6 hours

e) 6.2 hours

**5. The height of Ricky is 13 cm less than twice the height of Geoff. Also, Geoff is twice the height of Shane. The sum of heights of all three is 337 cm. Find the height of tallest among them.**

a) 120 cm

b) 167 cm

c) 187 cm

d) 157 cm

e) Cannot be
determined

**6. Harry and Ron started a business investing Rs. 50,000 and Rs. 35,000 respectively. Due to incompetent handling, they suffered a loss of Rs. 7480 at the end of one year. They hired Hermione 12 months after starting the business, on a promise to give 12% of profit as compensation for handling business. Hermione invested Rs. 25000 in the business. In the 2nd year, they covered all losses and made an additional profit of Rs. 4520. Find Harry’s earningfrom business at the end of two years.**

a) Rs. 3360

b) Rs. 400

c) Rs. 4800

d) Rs. 2055

e) None of
these

**7. The present ages of Neil, Nitin and Mukesh are in arithmetic progression. 8 years ago, the difference between ages of Neil and Mukesh was equal to the present age of Nitin. If the ratio of age of Mukesh 12 years later, and age of Neil 12 years ago is 7 : 1, then find the age of Nitin 6 years later.**

a) 48 years

b) 30 years

c) 54 years

d) 36 years

e) 42 years

**8. Snigdha won Rs. 80000 in lottery. She spent 30% of this money to buy a new laptop. She invested a part of the remaining amount in a scheme A and the rest in scheme B. Scheme A gives compound interest at 10% per annum, while scheme B gives simple interest at 15% per annum. She noticed that, the interest earned from scheme B was Rs. 208 more than that earned from scheme A at the end of 3 years. What is the difference in amounts invested in the two schemes?**

a) Rs. 24000

b) Rs. 32000

c) Rs. 40000

d) Rs. 8000

e) None of
these

**9. A mixture contains 3 qualities of tea, namely A, B and C in ratio 1 : 3 : 5 respectively. How much amounts of A and B should be added as percentages of their original amounts, so that the ratio of A, B and C in the mixture becomes 5 : 3 : 1?**

a) 200 and
2400

b) 2400 and
200

c) 400 and
200

d) 2400 and
400

e) None of
these

**10. The marked price of a headphone is Rs. 1800. A discount is offered on this frame. Accidentally, the cashier applied the discount twice while making the bill. As a result, it was sold at a price of Rs. 1152. Still, a profit of 20% is earned. Had the cashier applied discount only once, what would have been the percent profit?**

a) 40%

b) 24%

c) 50%

d) 4%

e) 60%

**Solutions:**

**1. C)**Let Kate got T marks and Stacy got (T – 2) marks.

If each of
them gets 3 marks more, then twice the product of their marks will be 1350 more
than the product of their actual marks.

⇒ 2(T + 3)(T +
1) = 1350 + T(T – 2)

⇒ 2T2 + 8T + 6 = 1350 + T2 – 2T

⇒ T2 + 10T – 1344 = 0

⇒ (T – 32)(T + 42) = 0

T will be 32
as T cannot be negative.

∴ Sum of marks
obtained by them = 32 + 30 = 62

**2. B)**Let the breadth of rectangle be B cm. So, length will be 2B cm.

Perimeter of
rectangle = 2(B + 2B) cm = 6B cm

The sum of
lengths of two adjacent sides of parallelogram is 40 cm.

⇒ Perimeter of
parallelogram = 2 × 40 cm = 80 cm

The perimeter
of rectangle is 50% more than that of parallelogram.

⇒ 6B = 80 × (1 + 50/100)

⇒ B = 120/6 =
20

∴ Area of
parallelogram = Half of area of rectangle = ½ × B × 2B = ½ × 20 × 40 = 400 square cm

**3. C)**Let the capacity of larger tank be T litres. So, capacity of smaller tank will be T/2 litres.

Initially,
larger tank is 30% full and smaller tank is empty.

∴ Amount of
water in larger tank = 30% of T = 0.3T

Now, 20
litres of water is transferred continuously for 40 minutes.

∴ Total amount
of water in larger tank = 0.3T – (20 × 40) = 0.3T – 800 litres

Total amount
of water in smaller tank = 800 litres

⇒ After the
transfer, they have equal percentage of water out of their respective total
capacities.

⇒[(0.3T−800)/T]×100
= [800/(T/2)] × 100

⇒ 0.3T = 2400

⇒ T = 8000
litres

∴ Capacity of
larger tank is 8000 litres.

**4. B)**Let speed of Nick be T km/hr and that of Harry be 2T km/hr.

When they are
running towards each other, the speed at which they are approaching will be 3T
km/hr.

To cover 42
km, they take 2.5 hours.

⇒ Speed =
Distance/Time

⇒ 3T = 42/2.5

⇒ T = 5.6

When they are
running in same direction, Harry will be chasing Nick at (2T – T) km/hr, i.e.,
T km/hr.

∴ Time taken
to chase Nick = Distance / Speed = 30 km/(5.6 km/hr) = 5.36 hours

**5. C)**Geoff is twice the height of Shane.

Let height of
Shane be T cm. So, height of Geoff will be 2T cm.

Let height of
Ricky be M cm.

The height of
Ricky is 13 cm less than twice the height of Geoff.

⇒ Height of
Ricky = M = 2 × 2T – 17 = (4T – 13) cm

Sum of heights
of all three = M + T + 2T = 4T – 13 + T + 2T = 337

⇒ 7T = 350

⇒ T = 50

Tallest among
them is Ricky, whose height is (4T – 13) cm, i.e., 187 cm.

**6. B)**Ratio of investments of Harry and Ron = 50000 : 35000 = 10 : 7

They suffered
a loss of Rs. 8500, which will be divided in the ratio of their investments,
i.e. 10 : 7.

Loss suffered
by Harry = 10/17 × 7480 = Rs. 4400

Loss suffered
by Ron = 7480 – 4400 = Rs. 3080

Now, Hermione
invested Rs. 25000 in the business.

∴ Ratio of
investments of Harry, Ron and Hermione = 50000 : 35000 : 25000 = 10 : 7 : 5

In the 2

^{nd}year, they covered all losses and made an additional profit of Rs. 4520.
∴ Total profit
made in 2

^{nd}year = 7480 + 4520 = Rs. 12000
Out of this,
12% is given to Hermione as a compensation for handling the business.

Hermione’s
income for handling business = 12% of 12000 = Rs. 1440

The remaining
profit will be divided among the three in ratio of their investments.

Remaining
profit = 12000 – 1440 = Rs. 10560

Harry’s share
in 2

^{nd}year’s profit = 10/22 × 10560 = Rs. 4800
Harry’s
earning in 2 years = 2

^{nd}year’s profit – 1^{st}year’s loss = 4800 – 4000 = Rs. 400**7. C)**The ages of Neil, Nitin and Mukesh are in arithmetic progression.

Let the
present ages of Neil, Nitin and Mukeshbr T – a, T and T + a respectively.

8 years ago
the difference between ages of Neil and Mukesh was equal to the present age of
Nitin.

∴ (T + a – 8) – (T – a – 8) = T

⇒ 2a = T

⇒ a = T/2

∴ Present age
of Neil = T – a = T – T/2 = T/2

And present
age of Mukesh = T + T/2 = 3T/2

As per given
condition, the ratio of age of Mukesh 12 years later, and age of Neil 12 years
ago is 7 : 1.

[(3T/2)+12]/[(T/2)
−12]=7/1

⇒ 3T/2 + 12 =
7T/2 – 84

⇒ 2T = 96

⇒ T = 48

∴ Present age
of Nitin = 48 years

⇒ Age of Nitin
6 years later = 48 + 6 = 54 years

**8. D)**Snigdha won Rs. 80000 in lottery, out of which she spent 30%.

∴ Remaining
amount = 70% of 80000 = 56000

Let’s assume
that the amount invested in scheme A is Rs. T.

∴ Amount
invested in scheme B = (56000 – T)

We know that,
Simple interest = P × R × T/100

And Compound
interest =

Where, P =
Principal, R = % rate of interest, T = number of years

As per given
information,

Simple
interest earned from scheme B was Rs. 208 more than the compound interest
earned from scheme A.

⇒ 450 × (56000 – T) – 331T =
208000

⇒ 25200000 – 450T – 331T = 208000

⇒ 781T =
24992000

⇒ T = 32000

∴ Amount
invested in scheme A = 32000

Amount
invested in scheme B = 56000 – 32000 = 24000

Required
difference = 32000 – 24000 = Rs. 8000

**9. D)**Ratio of A, B and C in the original mixture is 1 : 3 : 5.

Let’s assume
that the amounts of A, B and C are x, 3x and 5x respectively.

Now, after
adding some A and some B in the mixture, the new ratio of A : B : C becomes 5 :
3 : 1.

However, the
quantity of C remains unchanged, i.e. 5x.

∴ We can see
that, the amount of A and B in the new mixture must be: (5 × 5x = 25x) and (3 × 5x = 15x) respectively.

∴ Amount of A
added = 25x – x = 24x

∴ Amount of
added A as a percentage of original amount = 24x/x × 100 = 2400

Also, Amount
of B added = 15x – 3x = 12x

Amount of
added B as a percentage of original amount = 12x/3x × 100 = 400

Hence, the
required percentages are 2400 and 400.

**10. C)**On understanding the question statement properly, we observe that we are given selling price and profit percentage, and cost price can be easily found out with this information.

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

⇒ Cost price
of frame = Rs. 1152/(1 + (20/100)) = Rs. 1152/1.2 = Rs. 960

Now, let’s
assume that the discount available is D%.

Since the
cashier applied the discount twice accidentally, the selling price after
successive discounts = Marked price × (1 – (Discount %)/100) × (1 – (Discount
%)/100)

⇒ 1800 × (1 – D/100)

^{2}= 1152
⇒ 1152/1800 =
(1 – D/100)

^{2}
⇒ 1 – D/100 = 4/5 = 0.8

⇒ D = 20

Hence, the
available discount is 20%.

Has the
cashier applied the discount correctly,

Selling price
= 1800 × (1 – 20/100) = 1800 × 0.8 = Rs. 1440

In this case,
% profit = (1440 – 960)/960 × 100 = 50