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SSC GD Constable 17 February 2025 · Shift 3 · Elementary Mathematics — questions with answers · ShikshaSphere

Chapter 133 of 210

17 February 2025 · Shift 3

Elementary Mathematics

20 questions ~20 min readFree

20 questions

A car runs for one hour with a speed 60 km per hour, for 2 hours with a speed 70 km per hour and for 5 hours with a speed 50 km per hour. What is the average speed of the car in km per hour?

A.56.25
B.53.33
C.55.62
D.52.65

Solution

Average speed Average speed is total distance divided by total time, never the average of the speeds. Distance of each leg = speed

\times

time.

Total distance =60+140+250=450 km. Total time =1+2+5=8 hours. Average speed

= \frac{450}{8} = 56.25

km/h. So the correct option is (a).

Find the value of

((90 \div 5) \times (\frac{78}{6} + \frac{12}{1} \times (8 - 7)))

A.450
B.462
C.463
D.458

Solution

BODMAS simplification Work outwards from the innermost bracket (BODMAS). Inside the curly bracket:

\frac{78}{6} + \frac{12}{1} \times (8 - 7) = 13 + 12 \times 1 = 13 + 12 = 25

. Inside the round bracket:

90 \div 5 = 18

. Now multiply:

18 \times 25 = 450

. So the correct option is (a).

When the numbers 8651, 8018 and 7807 were divided by the greatest number x , then the remainder in each case was the same. The value of

x

is:

A.119
B.132
C.207
D.211

Solution

HCF, equal remainders If three numbers leave the same remainder when divided by x, then x divides every difference of those numbers exactly. So the greatest such x is the HCF of the differences.

633 = 3 \times 211

and

844 = 4 \times 211

, so

HCF (633, 211, 844) = 211

. Hence x=211. So the correct option is (d).

The ratio between the original price of a movie ticket and increased price of the movie ticket is 10 : 13. What is the increase in the revenue of the cinema hall, if the original price of the movie ticket was ₹250 and total 3600 tickets were sold as per the maximum capacity of the cinema hall that is 3600 persons?

A.₹2,70,000
B.₹1,28,000
C.₹82,000
D.₹1,98,000

Solution

Ratio and revenue Original : increased price =10:13. 10 units =₹250, so 1 unit

= \frac{250}{10} = ₹ 25

. Increased price

= 13 \times 25 = ₹ 325

. Increase per ticket =325-250=₹75. All 3600 seats were sold, so increase in revenue

= 75 \times 3600 = ₹ 2, 70, 000

. So the correct option is (a).

When the numbers 7807, 8022 and 8667 were divided by the greatest number x , then the remainder in each case was the same. The sum of the digits of x is:

Solution

HCF, equal remainders Equal remainders mean x divides each pairwise difference exactly, so the greatest x is the HCF of the differences.

645 = 3 \times 215

and

860 = 4 \times 215

, so

HCF (215, 645, 860) = 215

. Hence x=215. Sum of the digits =2+1+5=8. So the correct option is (a).

Two cyclists, M and N , start from the same point on a 1500 m circular track, cycling in opposite directions. M cycles at 18 km/hr and N at 22 km/hr. How long (in seconds) will it take for them to meet ?

A.132
B.127
C.130
D.135

Solution

Circular track, opposite directions Starting together and moving in opposite directions, they meet when the two of them together have covered one full lap, i.e. 1500 m.

Opposite directions, so relative speed =18+22=40 km/hr. 40 km/hr

= 40 \times \frac{5}{18} = \frac{100}{9}

m/s. Time to meet

= \frac{1500}{\frac{100}{9}} = 1500 \times \frac{9}{100} = 135

s. So the correct option is (d).

Find the value of

((25 \times 13) \times (2 \div 2 \times \frac{(16 - 13)}{3}))

A.344
B.313
C.325
D.312

Solution

BODMAS simplification Simplify the innermost bracket first (BODMAS). 16-13=3, so

\frac{(16 - 13)}{3} = \frac{3}{3} = 1

. Curly bracket

= 2 \div 2 \times 1 = 1 \times 1 = 1

. Round bracket

= 25 \times 13 = 325

. Now multiply:

325 \times 1 = 325

. So the correct option is (c).

The population of a district is 372000, out of which 168000 are males. 20% of the population is literate. If 20% males are literate, then what percentage of females are literate ?

A.20%
B.23%
C.18%
D.19%

Solution

Percentage, literacy Females =372000-168000=204000. Total literates

= 20 %

372000 = \frac{20}{100} \times 372000 = 74400

. Literate males

= 20 %

168000 = \frac{20}{100} \times 168000 = 33600

. Literate females =74400-33600=40800.

Required percentage

= \frac{40800}{204000} \times 100 = 20 %

. So the correct option is (a).

The average age of 26 students of a class is 43 years. If the age of the teacher is also included, the average age of the whole group becomes 44 years. The age (in years) of the teacher is:

A.68
B.72
C.67
D.70

Solution

Average, new member Total age of the 26 students

= 26 \times 43 = 1118

years. With the teacher there are 27 people, so their total age

= 27 \times 44 = 1188

years. Age of the teacher =1188-1118=70 years. Shortcut: the teacher lifts the average of 26 others by 1 year each, so his age

= 44 + 26 \times 1 = 70

years. So the correct option is (d).

Rodney sold 153 chairs and had a gain equal to the selling price of 63 chairs. What is his profit percentage ?

A.80%
B.75%
C.70%
D.65%

Solution

Profit on selling price Take the selling price of one chair as 1 unit, so SP of 153 chairs =153 units. Gain = SP of 63 chairs =63 units. CP = SP - gain =153-63=90 units. Profit % = gain ÷ CP

\times 100 = \frac{63}{90} \times 100 = 70 %

. Note the trap: dividing 63 by 153 would give the gain on the selling price, not the profit percentage. So the correct option is (c).

The salary of an employee is increased by

30 %

. By what percentage should the new salary be reduced in order to restore the original salary ? (Rounded off to 2 decimal places)

A.25%
B.27.02%
C.30%
D.23.08%

Solution

Percentage rise and fall Take the original salary as 100. After a rise of

30 %

the new salary =100+30=130. To get back to 100 the new salary must fall by 130-100=30. The fall is measured on the NEW salary, so reduction

% = \frac{30}{130} \times 100

= \frac{300}{13} = 23.0769 \dots \approx 23.08 %

So the correct option is (d).

Varun has ₹1230 with him. He divided it amongst his sons Ashish and Arun and asked them to invest it at

5 %

rate of interest compounded annually. It was seen that Ashish and Arun got same amount after 11 and 12 years respectively. How much (in ₹) did Varun give to Arun ?

A.600
B.450
C.730
D.630

Solution

Compound interest, equal amounts At

5 %

compounded annually, Amount

= P {(1 + \frac{5}{100})}^{n} = P {(\frac{21}{20})}^{n}

. Let Ashish get A and Arun get B. Their amounts are equal after 11 and 12 years:

A {(\frac{21}{20})}^{11} = B {(\frac{21}{20})}^{12}

\frac{A}{B} = \frac{21}{20}

, so A:B=21:20 - the son who invests longer gets less money. 21+20=41 units =₹1230, so 1 unit

= \frac{1230}{41} = ₹ 30

. Arun's share

= 20 \times 30 = ₹ 600

. So the correct option is (a).

Find the volume (in

{cm}^{3}

) of a cylinder with a diameter 6 cm and height 14 cm.

A.396
B.412
C.376
D.388

Solution

Volume of a cylinder The question gives the diameter, so halve it first: radius

= \frac{6}{2} = 3

cm.

Volume of a cylinder

= π r^{2} h

= \frac{22}{7} \times 3^{2} \times 14

= \frac{22}{7} \times 9 \times 14 = 22 \times 9 \times 2

= 396 {cm}^{3}

So the correct option is (a).

A, B and C can do a piece of work in 15 days, 30 days and 40 days, respectively. A starts working on the first day, A and B works on the second day and

A

and

C

works on the third day. This pattern is repeated till the work gets completed. In how many days will the work be over ?

A. $11 \frac{7}{11}$
B. $13 \frac{1}{4}$
C. $12 \frac{2}{5}$
D. $8 \frac{3}{5}$

Solution

Time and work, cyclic pattern Take the total work as

LCM (15, 30, 40) = 120

units. One day's work:

A = \frac{120}{15} = 8

B = \frac{120}{30} = 4

C = \frac{120}{40} = 3

units.

One cycle of 3 days =8+12+11=31 units. Three cycles =9 days

= 3 \times 31 = 93

units. Day 10 (A alone)

\to 93 + 8 = 101

; day 11 (A and B)

\to 101 + 12 = 113

units. Remaining =120-113=7 units, and day 12 belongs to A and C, who do 11 units a day. Extra time

= \frac{7}{11}

day. Total time

= 11 + \frac{7}{11} = 11 \frac{7}{11}

days. So the correct option is (a).

The marked price of a platinum ring is ₹52,300 and it is available for sale at two successive discounts of

20 %

and 4%. What is the selling price (in ₹) of the platinum ring ? (Round off to the nearest rupee.)

A.40,200
B.40,033
C.40,166
D.40,233

Solution

Successive discounts Successive discounts are applied one after the other, so the multipliers multiply. SP

= 52300 \times \frac{100 - 20}{100} \times \frac{100 - 4}{100}

= 52300 \times \frac{80}{100} \times \frac{96}{100}

= 41840 \times \frac{96}{100} = 40166.4

Rounded to the nearest rupee, SP =₹40,166. Adding the discounts to get

24 %

would give ₹39,748, which is why that shortcut fails. So the correct option is (c).

A shopkeeper bought an article for ₹540. At what price (in ₹) should he sell the article to make

10 %

profit ?

A.606
B.594
C.582
D.486

Solution

Profit percentage SP = CP

\times (1 + \frac{profit}{100})

, with profit =10.

= 540 \times (1 + \frac{10}{100}) = 540 \times \frac{110}{100}

=594 So the article must be sold for ₹594, i.e. option (b).

The force acting on an object is directly proportional to its mass. If a force of 10 N is required to move an object of mass 2 kg , what force (in newtons) is needed to move an object of mass 5 kg ?

A.25
B.30
C.20
D.15

Solution

Direct proportion

F \propto m

means

\frac{F}{m}

stays constant, so

\frac{F_{1}}{m_{1}} = \frac{F_{2}}{m_{2}}

\frac{10}{2} = \frac{F_{2}}{5}

F_{2} = 5 \times 5 = 25

So the required force is 25 N, i.e. option (a).

Two trains having lengths of 450 m and 350 m are running at speeds of 80

km / h

and

110 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.2.4
B.3.4
C.1.6
D.3

Solution

Trains crossing, same direction To cross completely, the faster train must cover the sum of the two lengths. Distance =450+350=800 m.

Same direction, so relative speed =110-80=30 km/h. 30 km/h

= 30 \times \frac{5}{18} = \frac{25}{3}

m/s. Time

= \frac{800}{\frac{25}{3}} = 800 \times \frac{3}{25} = 96

s. The answer is asked in minutes:

\frac{96}{60} = 1.6

minutes. So the correct option is (c).

Rakesh invests a sum of ₹5400 and Shivam invests a sum of ₹10200 at the same rate of simple interest per annum. If, at the end of 4 years, Shivam gets ₹480 more interest than Rakesh, then find the rate of interest per annum (in percentage).

A.2.5
B.3.5
C.1.5
D.4.5

Solution

Simple interest, rate Simple interest

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

, and here R and T=4 are the same for both men. So the extra interest comes only from the extra principal. Extra principal =10200-5400=₹4800.

\frac{4800 \times R \times 4}{100} = 480

192R=480

R = \frac{480}{192} = 2.5

So the rate is

2.5 %

per annum, i.e. option (a).

Veer has ₹1632 with him. He divided it amongst his sons Nitin and Pravin and asked them to invest it at 4% rate of interest compounded annually. It was seen that Nitin and Pravin got same amount after 12 and 13 years respectively. How much (in ₹) did Veer give to Nitin ?

A.800
B.832
C.682
D.900

Solution

Compound interest, equal amounts At

4 %

compounded annually, Amount

= P {(1 + \frac{4}{100})}^{n} = P {(\frac{26}{25})}^{n}

. Let Nitin get N and Pravin get P; their amounts are equal after 12 and 13 years:

N {(\frac{26}{25})}^{12} = P {(\frac{26}{25})}^{13}

\frac{N}{P} = \frac{26}{25}

, so Nitin : Pravin =26:25. 26+25=51 units =₹1632, so 1 unit

= \frac{1632}{51} = ₹ 32

. Nitin's share

= 26 \times 32 = ₹ 832

. So the correct option is (b).

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