# Free Basic Arithmetic - 03 Practice Test - CAT

### Question 1

Which is the least number, which when subtracted from both the numerator and the denominator of the ratio 8070, gives 1311?

#### SOLUTION

Solution :C

Solving conventionally,

Let x be the required number

80−x70−x=1311

880 – 11x = 910 – 13x

2x = 30

x= 15

Shortcut:- Use answer options. Always start with the middle answer option

### Question 2

Anju’s and Binoy’s marks are in the ratio 3:5. If each gets 20 marks more, the ratio becomes 13:21. Find Anju’s marks?

#### SOLUTION

Solution :B

3:5 ⇒ 3x and 5x

Now, it’s given that

(3x+20)5x+20=1321

Cross multiplying; 63x + 420 = 65x + 260 So, x= 80

The marks will therefore be: Anju: 3x=3×80=240 and Binoy: 5x=5×80=400.

### Question 3

There is a bag with a mixture of sugar, rice and wheat grains. The quantity of rice is 45th that of wheat and the quantity of sugar is 34th that of rice. In 12 kg of the mixture how much wheat and sugar will be there?

#### SOLUTION

Solution :C

Answer = Option c

If we take the amount of Sugar as 3x, then Rice = 4x and Wheat = 5x (ratio = 3:4:5; as rice= 45 wheat and sugar = 34 rice)

12x= 12 x=1

Wheat = 5 kg and Sugar = 3 kg. Total = 8 kg

### Question 4

There are 5 friends in a class who get marks in the ratio 3:4:5:6:7. The maximum marks are the same in each case. The total marks obtained by the 5 are 35th the maximum obtainable marks. How many friends got more than 70% of the total marks?

#### SOLUTION

Solution :C

Lets assume that the maximum marks are 100. total marks available =500

Total marks obtained by all 5 together =35×500=300

Which is divided in the ratio 3:4:5:6:7

Marks are 36, 48,60, 72 and 84. only 2 students get more than 70%.

### Question 5

The charges for a graphics designer is partially fixed and partially variable with the number of hours. The charge is Rs.550 for 4.5 hours and Rs.300 for 2 hours. Find the charges of 1 hour?

#### SOLUTION

Solution :B

The total charge = Fixed component +Variable component

Z= F+kx

Where F and x are fixed

550 =F +k(4.5)

300=F + k(2)

Solving simultaneously, F= 100 and k= 100

Charges for 1 hour = 100 +1(100) =200

### Question 6

There are 2 baskets with n identical balls. Half the balls from basket 1 are put into basket 2. The ratio of balls in Basket 1 to Basket 2 gets reversed. Next 13rd and 23rd of the balls from the 1st basket and 2nd basket respectively are exchanged. The ratio of balls in basket 2 to basket1 is?

#### SOLUTION

Solution :D

Option (d)

=23b+23a13b+13a=2:1

Required ratio(basket 2: basket 1) = 1:2

### Question 7

Till the age of 21, Arun grows such that his height varies as the square root of this age. When Arun is 9 years old, his height is 4 feet. What is his height at 16 years?

#### SOLUTION

Solution :C

Option (c)

Relationship given:-

4=K√9→K=43

Hα√AH=K√A

Height of Arun at 16 years H=43×4=163 = 5 feet 4 inches

### Question 8

Speed of A is twice that of B. Both start from a point X towards a point Y. If B took 3 hours more than A, what is the time taken by B?

#### SOLUTION

Solution :B

Distance is constant, speed and time are inversely proportional. Therefore, if ratio of speed of A and B is 2:1, ratio of time taken will be 1:2

Time taken by A= X

Time taken by B= 2x

2X-X=3

x=3. B takes 6 hours

### Question 9

A sum of Rs 530 is divided between P,Q,R such that P gets 12 that of Q and Q gets twice that of R. What is the ratio of Q to that of the sum of P and Q?

#### SOLUTION

Solution :B

P=12Q; Q=2R or PQ=12; QR=21

Shares of P, Q, R = x, 2x,x

QP+Q=2x3x=2:3

### Question 10

P,Q,R invested Rs 1000, Rs 600 and Rs 400 respectively to start a business. The profit is Rs 200 which is to be divided among P,Q,R in the ratio of their capital invested. What share does R get?

#### SOLUTION

Solution :C

R’s share of Profit =210×200=Rs.40

### Question 11

A, B and C went for lunch to a restaurant. A had 100withhim,Bhad60 and C had 409.Theygotabillfor104 and decided to give a tip of $16. They further decided to share the total expenses in the ratio of the amounts of money each carried. The amount of money, which C paid more than what A paid, is

#### SOLUTION

Solution :C

They divided the bill in the ratio of money they carried.

So, 120 got divided A= 21, B= 12.65, C= 86.25. C paid 65.25 more than A.Option (3).

### Question 12

One year payment to the servant is Rs. 200 plus one shirt. The servant leaves after 9 months and receives Rs.120 and a shirt. Then find the price of the shirt.

#### SOLUTION

Solution :C

Solution:At the first glance it seems that the answer is cannot be determined but let’s investigate further. Let the price of the shirt be 12X, where every month he earns 112th of the shirt price plus his wages.He earns 20012 every month as salary .. So in 9 months he should've earned 150 cash. But he only got 120 hence Rs.30 went to his shirt deduction.Therefore 3X= 30 & 12X= 120. Option (c).

### Question 13

‘a’ and ‘b’ are any two distinct numbers belonging to the set {1,2,3,4,5,6}. How many ratios of the form ab can be formed which are not integers.

#### SOLUTION

Solution :C

For each A selected there are five ways of selecting a B.. There are total 30 ratios that can be formed. Now for ‘1’ there are 5 numbers that can come in the numerator to form an integer.

For 2 there are 2 numbers and for 3 there is only one.

Therefore 30-5-2-1= 22 is the answer.

### Question 14

Picnic invites two kinds of charges: bus fare, which is independent of the number of people attending the picnic and buffet lunch, which increases directly with an increase in the number of people. The charges are calculated to be Rs. 165 per head when there are 200 invitees and Rs. 170 per head when there are 150 invitees. What would be the charges per head when there are 100 invitees?

#### SOLUTION

Solution :B

Ans. (b) Let the bus fare = Rs. x

and buffet lunch per head = Rs. y

x+200y=165×200.......(i)

x+150y=170×150.......(ii)

Then, x+100y=2×(ii)−(i)=51000−33000=18000

Therefore, Cost per head = Rs. 180

### Question 15

Mayawati buys two elephants for 40,000 each, She sells one at a profit of 20% and other at a loss of 20% . What is her profit/ loss percentage?

#### SOLUTION

Solution :D

20% of 40,000 = 8000.

Profit = loss = 8000.Hence, No Profit, No loss; Option (d).