# Free Basic Arithmetic - 02 Practice Test - CAT

### Question 1

At a new book-store, the inaugural discount is as follows. If the value of purchase < 3200, the buyer gets a 14% discount. If the purchase 3200<x<6300 , then the buyer gets a 16% discount. Above 6300, the discount percentage is x. A certain buyer gets a total discount of Rs. 1520 which is 16% of the purchase value. What is x?

#### SOLUTION

Solution :C

16% of purchase value = Rs. 1520

purchase value = 9500

1520=14% of 3200+16% of 3100+x% of 3200

1520=944+x% of 3200

576=x% of 3200

x=18%

### Question 2

It is given that two types of rice A and B costing Rs.3 and 3.30 per kg respectively are mixed to form a mixture costing Rs.3.20 per kg. Find the proportion in which they are mixed to obtain this Cost price?

#### SOLUTION

Solution :D

option (d)

We can solve this question using alligation.

Ratio = 0.10 : 0.20= 1:2

### Question 3

Two alloys containing copper and zinc are in the ratios 5:8 and 5:3.If they are melted in equal quantities, The ratio of Zinc to copper in the resultant alloy is?

#### SOLUTION

Solution :D

CopperZinc=513+58313+38=105:103Solving using alligation

With respect to zinc

Now use answer options to get the value of x =103:105

### Question 4

In a particular school, the maximum marks in a subject is 250. Suppose a student obtained 60% marks, what were his actual marks?

#### SOLUTION

Solution :C

Actual =60% of 250=60100×250=604×10=6004=150

### Question 5

The length of a rectangle is increased by a=30% and breadth is decreased by b=25% . What is the percentage change in the area of the rectangle?

#### SOLUTION

Solution :B

Answer = option b

Initial area =l×b

Final area =1.3l×0.75b

=0.975l×b

% change =(1−0.975)×100=2.5% decrease

### Question 6

Ram Lal invested a certain amount for three years, under compound interest compounded annually and received Rs.17820. If he had invested the same amount for six years at the same rate of interest compounded annually, he would have received Rs.49410. What amount (in Rs.) did he invest?

#### SOLUTION

Solution :D

Let the sum be P and the interest rate be r.

Then after ‘n’ years A=P(1+r100)n=PRn where R=1+r100

Now, 17820=PR3 , 49410=PR6

R3=4941017820So, P=17820×1782049410 =Rs.6427

### Question 7

A trader makes a profit equal to the selling price of 50 articles when he sold 80 of the articles. What % profit did he make in the transaction?

#### SOLUTION

Solution :D

Soln:Let S be the selling price of 1 article.Therefore, the selling price of 80 articles = 80 S

The profit earned by selling these 80 articles = selling price of 50 articles = 50 S

We know that Selling Price (S.P.) = Cost Price (C.P) + Profit of Selling price of 80 articles = 80 S and Profit = 50 S

80 S = C.P + 50 S. Hence, C.P = 80 S - 50 S = 30 S.Profit %=(50 S30 S)×100=166.67%

### Question 8

Ram adjusted his electronic weighing scale in a typical way. But he gives a discount of 10% in every transaction. His weighting scale shows 5 kg for 4 kg. What is the actual profit % when the displayed weight is 10 kg, if he sells the commodity at its cost price?

#### SOLUTION

Solution :A

5kg ---> 4kg

10kg ---> 8kg

C.P of product of 1 kg = x

Total C.P = 8x

S. P = 10x - x(10% discount of 10x)

= 9x

Profit % = x8x×100

= 12.5%

### Question 9

In a village which has a barter system, 1 kg of rice is equivalent to 1 dozen bananas. Anil gives 1.5 kg rice to Binod using a false weight of 800 gm as 1 kg and takes 15 bananas. Who is in profit and what is the percentage profit?

#### SOLUTION

Solution :A

Soln:

800 gm ==1 kg ,1.5 kg == 1.2 kg

Anil actually sold 1.2 kg rice and so he should get 1.2×12=14.4 bananas but he got 15 bananas. So, Anil is making a profit of 0.6 which is 4.17%.

Hence option (a).

### Question 10

At what price should I buy a share whose face value is Rs.200 and pays dividend of 9%, so that my yield is 12%

#### SOLUTION

Solution :C

Let the required price be Rs. x

Dividend = 9% of Rs. 200 = Rs. 18

0.12x = 18 ⇒ x = Rs. 150

Hence option (c)

### Question 11

Ravi bought a bike with a marked price of Rs.40,000. The dealer gave him two successive discounts of 10% and 20% . After he bought the bike, he spent

10% of the cost of the bike on the accessories. At what price should he sell the bike to earn a profit of 10%.

#### SOLUTION

Solution :D

Cost of the bike = 0.9×0.8×40000 = Rs. 28800

For Ravi total cost =28800+(28800×0.1)=31680

So, for a profit of 10% he should sell the bike at 31680+(0.1×31680)=Rs.34848

Hence option (d)

### Question 12

Two cars are of the same cost price. One is sold at a profit of 15% and the other for Rs. 23000 more than the first. If the net profit is 20% , find the cost price of each car.

#### SOLUTION

Solution :B

Let the cost price be ‘p’ then

2 (1.15 P) + 23000 = 2 (1.2 P)

0.1 P = 23000

P = Rs.230000

Hence option (b)

### Question 13

A bank gives out Rs.6000 to Customer A for 2 years and Rs.1500 to customer B for 4 years. It receives interest of Rs.900 from them put together. Find the rate of interest (SI)?

#### SOLUTION

Solution :A

Rs.6000 for 2 years Rs.12000 for 1 year and Rs.1500 for 4 years Rs.6000 for 1 year

Total Principal = Rs 18000 for 1 year

SI=PRT100→Rate=900×10018000=5%

### Question 14

Alok borrows some money from the bank and the SI on the sum is 19th the principal amount and the number of years is the rate of interest. Find r?

#### SOLUTION

Solution :C

Answer = Option c

Principal = P

Time = x

Rate = x

SI=P9

SI=PRT100P9=Px2100

x2=1009⇒x=103=3.33%

### Question 15

A nano car is bought in 2012 for Rs.17576, if it’s value appreciates annually by 4%, what was its value three years ago?

#### SOLUTION

Solution :B

Price three years ago X×(104100)3 = present price

Price 3 years ago = X = 17576(1.04)3

Price 3 years ago= X = 17576×25×25×2526×26×26 = Rs15625 . Option (2).