For Parents For Educators & Experts For Institutions For Employers

SSC GD Constable 7 February 2025 · Shift 2 · Elementary Mathematics — questions with answers · ShikshaSphere

Chapter 53 of 210

7 February 2025 · Shift 2

Elementary Mathematics

20 questions ~20 min readFree

20 questions

A salesman offers a discount scheme of 'Buy 25 and get 5 free' on the purchase of notebooks in his shop. He professes that a notebook costs him ₹10, but in reality, it costs him ₹5. Find the difference between his profit percentage and scheme discount.

A.42%
B.48%
C.50%
D.56%

Solution

Discount scheme and profit In the scheme a customer pays for 25 notebooks and carries home 30 notebooks.

Selling price of the lot (in ₹)

= 25 \times 10 = 250

Real cost of the lot (in ₹)

= 30 \times 5 = 150

Profit (in ₹) = 250 - 150 = 100 Profit percentage

= \frac{100}{150} \times 100 = 66 \frac{2}{3} %

Scheme discount

= \frac{5}{30} \times 100 = 16 \frac{2}{3} %

Required difference

= 66 \frac{2}{3} % - 16 \frac{2}{3} % = 50 %

Hence the correct option is (c).

If the mean proportional of 18 and 98 is 2A + 6, the value of A is:

A.16
B.19
C.18
D.17

Solution

Mean proportional The mean proportional of a and b is

\sqrt{a b}

\sqrt{18 \times 98} = \sqrt{1764} = 42

2A + 6 = 42 2A = 42 - 6 = 36

A = \frac{36}{2} = 18

Hence the correct option is (c).

The third proportional of (X^2.5/Y^1.5) × Z^3.5 and X^0.25 × (Y^0.25/Z^(-0.25)) is:

A. $\frac{Y^{3}}{X^{3} Z^{3}}$
B. $\frac{Y^{2}}{X^{2} Z^{3}}$
C. $\frac{Y^{2}}{X^{2} Z^{2}}$
D. $\frac{Y^{2}}{X^{3} Z^{2}}$

Solution

Third proportional with indices If c is the third proportional of a and b, then a:b::b:c, so

c = \frac{b^{2}}{a}

Here

a = \frac{X^{2.5}}{Y^{1.5}} \times Z^{3.5} = X^{2.5} Y^{- 1.5} Z^{3.5}

and

b = X^{0.25} \times \frac{Y^{0.25}}{Z^{- 0.25}} = X^{0.25} Y^{0.25} Z^{0.25}

b^{2} = X^{0.5} Y^{0.5} Z^{0.5}

c = \frac{b^{2}}{a} = X^{0.5 - 2.5} Y^{0.5 + 1.5} Z^{0.5 - 3.5}

= X^{- 2} Y^{2} Z^{- 3} = \frac{Y^{2}}{X^{2} Z^{3}}

Hence the correct option is (b).

The distance from Chandigarh to Amritsar is covered in 4.5 hours at a speed of 50 km/hr. By how much should the speed (in km/hr) be increased to save 30 minutes of travel time?

A.6.75
B.6
C.6.5
D.6.25

Solution

Speed, time and distance Formula:

D = S \times T

D = 50 \times 4.5 = 225

km New time = 4.5 - 0.5 = 4 hours New speed

= \frac{225}{4} = 56.25

km/hr

Increase in speed = 56.25 - 50 = 6.25 km/hr Hence the correct option is (d).

The price (per litre) of petrol increases by 40%. By what percent should its consumption be reduced such that the expenditure on it increases by 19% only?

A.15%
B.85%
C.84%
D.18%

Solution

Percentage change in consumption Formula:

E = P \times C

Let the price and the consumption both be 100, so

E = 100 \times 100 = 10000

New price = 140 and new expenditure = 11900 New consumption

= \frac{11900}{140} = 85

Fall in consumption = 100 - 85 = 15 Required reduction

= \frac{15}{100} \times 100 = 15 %

Hence the correct option is (a).

Evaluate: (-9) - (-60) ÷ (-15) + (-3) × 6

A.-31
B.-34
C.-30
D.-33

Solution

BODMAS with integers Apply BODMAS: division and multiplication before addition and subtraction.

(- 9) - (- 60) \div (- 15) + (- 3) \times 6

(- 60) \div (- 15) = 4

and

(- 3) \times 6 = - 18

= (-9) - 4 + (-18) = -9 - 4 - 18 = -31 Hence the correct option is (a).

The average age of 40 students of a class is 12 years. If the age of the teacher is also included, the average age of the whole group becomes 13 years. The age (in years) of the teacher is:

A.50
B.51
C.53
D.56

Solution

Average with a new member Total age of 40 students

= 40 \times 12 = 480

years With the teacher the group has 41 members. Total age of the group

= 41 \times 13 = 533

years Age of the teacher = 533 - 480 = 53 years Shortcut: age = new average + (number of students

\times

rise)

= 13 + 40 \times 1 = 53

Hence the correct option is (c).

The average age of 35 students in a group is 15 years. When the teacher's age is included, the average age of the group increases by 1.25 years. What is the teacher's age (in years)?

A.45
B.60
C.55
D.50

Solution

Average with a new member Total age of 35 students

= 35 \times 15 = 525

years New average = 15 + 1.25 = 16.25 years Total age of 36 members

= 36 \times 16.25 = 585

years Age of the teacher = 585 - 525 = 60 years Hence the correct option is (b).

The simple interest on a principal amount (in ₹) is ₹524 for a period of 2 years at the rate of 5% per annum. The principal amount (in ₹) is:

A.5240
B.5239
C.5249
D.5234

Solution

Simple interest Formula:

S I = \frac{P \times R \times T}{100}

524 = \frac{P \times 5 \times 2}{100}

524 = \frac{10 P}{100} = \frac{P}{10}

P = 524 \times 10 = 5240

Hence the correct option is (a).

The diagonals of a rhombus are 4 m and 6 m, respectively. Find its area (in m²).

A.9
B.12
C.18
D.24

Solution

Area of a rhombus

Formula: area of a rhombus

= \frac{1}{2} \times d_{1} \times d_{2}

= \frac{1}{2} \times 4 \times 6

Area

= 12 m^{2}

Hence the correct option is (b).

Ajay invested some money in HDFC at 4% per annum rate of interest. What would be the corresponding simple interest (in ₹) if after 2 years, Ajay got ₹204 as compound interest, considering annual compounding?

A.215
B.200
C.210
D.195

Solution

Compound and simple interest Effective compound interest rate for 2 years

= r + r + \frac{r \times r}{100}

= 4 + 4 + \frac{4 \times 4}{100} = 8.16 %

8.16 %

of the principal = 204

P = \frac{204 \times 100}{8.16} = 2500

S I = \frac{P \times R \times T}{100} = \frac{2500 \times 4 \times 2}{100} = 200

Hence the correct option is (b).

If the income of Ravi is 24% more than that of Ram, then by what percentage is the income of Ram less than that of Ravi?

A. $\frac{700}{31}$
B. $\frac{600}{31}$
C. $\frac{400}{31}$
D. $\frac{500}{31}$

Solution

Percentage comparison If A is

x %

more than B, then B is

\frac{x}{100 + x} \times 100 %

less than A. Here x = 24, so Ram's income is less by

\frac{24}{100 + 24} \times 100 %

= \frac{24}{124} \times 100 = \frac{2400}{124}

= \frac{600}{31}

Hence the correct option is (b).

The greatest number, which divides 1477 and 671 to leave 0 and 6 respectively as remainders, is:

A.17
B.16
C.20
D.7

Solution

HCF with remainders A divisor that leaves remainder r in N divides N - r exactly. So the number divides 1477 - 0 = 1477 and 671 - 6 = 665

Required number = HCF of 1477 and 665 = 7 Check: 7 > 6, so a remainder of 6 is possible. Hence the correct option is (d).

Pramod sold 154 chairs and had a gain equal to the selling price of 54 chairs. What is his profit percentage?

A.64%
B.59%
C.49%
D.54%

Solution

Gain stated in selling price SP of 154 chairs - CP of 154 chairs = SP of 54 chairs So CP of 154 chairs = SP of 154 - 54 = 100 chairs Let the SP of one chair be ₹1. Then CP of 154 chairs = 100 and SP of 154 chairs = 154 Profit = 154 - 100 = 54 Profit percentage

= \frac{54}{100} \times 100 = 54 %

Hence the correct option is (d).

A shopkeeper bought an article for ₹520. At what price (in ₹) should he sell the article to make 20% profit?

A.612
B.636
C.624
D.416

Solution

Selling price for a given profit Formula:

S P = C P \times \frac{100 + p}{100}

, where p is the profit percentage.

S P = 520 \times \frac{100 + 20}{100}

= 520 \times \frac{120}{100}

= 624 Hence the correct option is (c).

Two trains having lengths of 340 m and 360 m are running at speeds of 80 km/h and 90 km/h, respectively, in the same direction. The time taken (in minutes) by the faster train, coming from behind, to completely cross the other train is:

A.7
B.4.2
C.3.7
D.6

Solution

Relative speed of trains

Same direction, so relative speed = 90 - 80 = 10 km/h 10 km/h

= 10 \times \frac{5}{18} = \frac{25}{9}

m/s Distance to be covered = 340 + 360 = 700 m Time

= \frac{700 \times 9}{25} = 252

seconds Time in minutes

= \frac{252}{60} = 4.2

Hence the correct option is (b).

Krish has ₹1224 with him. He divided it amongst his sons Veer and Nitin and asked them to invest it at 4% rate of interest compounded annually. It was seen that Veer and Nitin got same amount after 12 and 13 years respectively. How much (in ₹) did Krish give to Nitin?

A.624
B.600
C.450
D.724

Solution

Equal compound amounts Formula:

A = P {(1 + \frac{r}{100})}^{n}

Let Veer get V and Nitin get N, so V + N = 1224 Equal amounts:

V {(1 + \frac{4}{100})}^{12} = N {(1 + \frac{4}{100})}^{13}

\frac{V}{N} = 1 + \frac{4}{100} = \frac{26}{25}

Nitin's share

= \frac{25}{26 + 25} \times 1224 = \frac{25}{51} \times 1224 = 600

Hence the correct option is (b).

Evaluate:

32 \div 8 \times 4 - 3 \times 3

A.9
B.6
C.7
D.10

Solution

BODMAS order of operations Apply BODMAS: division and multiplication from left to right, then subtraction.

32 \div 8 \times 4 - 3 \times 3

32 \div 8 = 4

, so

4 \times 4 = 16

3 \times 3 = 9

= 16 - 9 = 7 Hence the correct option is (c).

The greatest number, which divides 943 and 1957 to leave 7 and 1 respectively as remainders, is:

A.12
B.28
C.10
D.13

Solution

HCF with remainders A divisor that leaves remainder r in N divides N - r exactly. So the number divides 943 - 7 = 936 and 1957 - 1 = 1956

Required number = HCF of 936 and 1956 = 12 Check: 12 > 7, so both remainders are possible. Hence the correct option is (a).

A and B can do a work in 30 days and 10 days, respectively. If they work on alternate days starting with A, then in how many days will the work be completed?