Arithmetic(Exams > Cat > Quantitaitve Aptitude ) Questions and answers for exam Preparation

Exams > Cat > Quantitaitve Aptitude

ARITHMETIC MCQs

Total Questions : 147 | Page 12 of 15 pages

Ravi took a loan of Rs. 1 Lakh from SBI at the rate of $6 %$ per annum of simple interest for 10 years. After some time, the rate of interest dropped down to $4 %$ and as a result, Ravi paid only Rs. 1.48 lakhs at the end of the loan period. Number of years after which the rate of interest was decreased to $4 %$ is___

Discuss Question

Answer: Option A. ->
:
He paid Rs. 48,000 interest in 10 years.

$\frac{48, 000}{1, 00, 000} \times 100 = 48 %$ in 10 years. So, $4.8 %$ in a year.

After 4 years the rate of interest was decreased to $4 %$

Question 112.

Sajan lent Rs. 7000 to two of his friends: to one at $4 %$ and to other at $6 %$ SI. The total amount received as interest by Sajan after 3 years is Rs. 996. Find the amount lent at $6 %$ .

Rs. 1300
Rs. 2600
Rs. 4400
Rs. 1600

Discuss Question

Answer: Option B. -> Rs. 2600
:
B

Principal = Rs. 7000

Interest Received = Rs. 996

So, average rate $= \frac{(996 \times 100)}{3 \times 7000} = \frac{166}{35} %$

Now apply alligation:

So, the ratio in which the money was lent at $4 %$ and $6 %$ is 22: 13

So, the amount lent at $6 %$ = Rs. 2600. Hence option (b)

Alternatively: the question can be solved using answer options.

Question 113.

The compound interest on a certain sum for 2 years is Rs. 756 and simple interest is Rs. 720. Now, If the sum is invested such that the SI is Rs. 1296 and the number of years is equal to the rate percentage per year, then find the rate per cent:

Discuss Question

Answer: Option C. -> 6
:
C

It is given that simple interest for 2 years = Rs. 720

So, for 1 year = Rs. $\frac{720}{2}$ = Rs. 360 (because it is SI)

Compound Interest for 2 year = Rs. 756

Difference in the interest = Rs. 36 (756-720)

This difference is the interest on the interest of the first year.

So rate of interest $= (\frac{36}{360}) \times 100 = 10 %$

Now the interest for $1^{s t}$ Year = Rs. 360 at $10 %$ SI

So, principal for $1^{s t}$ year = Rs. 3600

We have, $S I = \frac{(P \times R \times T)}{100}$

$\frac{3600 \times k^{2}}{100} = 1296$

k = 6

Question 114.

Of the two machines purchased, the first one’s share of cost is $37.5 %$ . Depreciation is to be calculated annually at the rates of $20 %$ and $15 %$ on the first and second machines respectively, of the value of each machine at the beginning of the year. At the end of two years, the total value of depreciation is what percent of the total cost?

$32.94 %$
$33.36 %$
$30.84 %$
Can’t be determined

Discuss Question

Answer: Option C. ->

30.84 %

:
C

Let the cost of two machines be Rs. 800

So, cost of $1^{s t}$ machine = $37.5 %$ of Rs. 800 = Rs. 300

Cost of $2^{n d}$ machine = $62.5 %$ of Rs. 800 = Rs. 500

Total cost of 2 machines at the end of 2 yrs = 553.25

Total depreciation $= 246.75 = (\frac{246.75}{800}) \times 100 = 30.84 %$

Hence option (c)

Question 115.

A $10 %$ solution is one in which 10 gm of solute is dissolved in 100 gm of water. On heating the solution water evaporates. So, 1 kg of the $10 %$ solution is reduced to 0.4 kg. What is its concentration now?

$32.6 %$
$14.8 %$
$22.7 %$
$29.4 %$

Discuss Question

Answer: Option D. ->

29.4 %

:
D

In a $10 %$ solution, in 110 gm of solution there is 10gm of solute.

So, 1 kg of solution has $1 \times \frac{10}{110} = \frac{1}{11}$ kg of solute.

After heating, amount of solution = 0.4 kg

So, amount of water $= \frac{2}{5} - \frac{1}{11} = \frac{17}{55}$ kg

Solution percentage $= (\frac{1}{11}) \times (\frac{55}{17}) \times 100 = 29.4 %$

Question 116.

When price of wheat increased by $44 %$ , a family reduced its consumption in such a way that the expenditure on wheat is only $20 %$ more than before. If 60 kg of wheat was the previous consumption. The decrease in the consumption is___

Discuss Question

Answer: Option D. ->

29.4 %

Method 1:

$Q u a n t i t y \times R a t e = P r i c e$

Given : Q1= 60

R1 =r

P1= p

Q2=q

R2=1.44r

P2=1.2p

Hence Q=50

So the difference in price is 50.

Method 2:

Let the price per kg of wheat = Rs 10, hence total expenditure initially = Rs 600

The expenditure increases by $20 %$ = Rs 720

Also, the price increases by $44 %$ , hence price per kg = 14.4

Thus, new consumption $= \frac{720}{14.4}$ = 50 kgs. the diffrence in consumption is 60-50= 10 kg. Option (a)

Question 117.

A particular shop sells goods at cost. A person buys goods worth Rs.60 from the shop and gives the shopkeeper a Rs.100 note. As the shopkeeper does not have change to give his customer, he exchanges this Rs.100 note for 6 Rs.10 notes and 2 Rs. 20 notes from the bank to settle accounts with the customer. The next day, the banker returns the Rs.100 note claiming it to be a counterfeit and takes two Rs.50 notes from the shopkeeper. If the note was actually a counterfeit, what is the total loss to the shopkeeper?

Rs. 200
Rs. 130
Rs. 100
Rs. 60

Discuss Question

Answer: Option C. -> Rs. 100
:
C

The shopkeeper has lost Rs.100 only. The entire transaction can also be viewed as the shopkeeper getting a counterfeit Rs.100 note against which he has given goods worth Rs.60 and change worth Rs.40.

Question 118.

A group of 80 People play atleast one of the games- carrom, snooker and TT. 40 play carrom, 50 play snooker and 35 play TT. If 14 people play both Carrom and Snooker, 20 people play both Snooker and TT and 12 people play both TT and carrom, find the ratio of the number of people who play carrom only to the number who play only TT?

17:4
13:1
15:4
10:1

Discuss Question

Answer: Option C. -> 15:4
:
C

Answer Option - C

x- number who play all 3 games

80= 125 –(14+12+20) +x

x= 1, the venn diagram can be represented as

Thus ratio=15:4

Question 119.

What is the total number of students who opted for only football?

40
80
90
Cannot be determined

Discuss Question

Answer: Option D. -> Cannot be determined
:
D

Question 120.

In a class of 200 students who play cricket and hockey, the number of students who play neither of the games is 16 less than those who play both. The number of students who do not play cricket is 24 more than those who do not play hockey.
The number of students who play hockey is ___.

Discuss Question

Answer: Option D. -> Cannot be determined
: