CDS Maths(1) Questions and answers

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Exams

These are the list of questions asked in the previous year CDS Maths Exams. You can practice these questions as real time exam in this link.

1). Pipe A can fill a tank in 3 hours. But there is a leakage also, due to which it takes 3.5 hours for the tank to be filled. How much time will the leakage take in emptying the tank if the tank is tilled initially?

A). 21 hours

B). 20 hours

C). 18 hours

D). 10.5 hours

View Answer

Correct Answer: 21 hours

Part of tank filled by pipe A in 1hr = \( \Large \frac{1}{3} \)

and let the part of tank supplied by another pipe 1 in 1 hr = \( \Large \frac{1}{x} \)

Now, according to question-

\( \Large \frac{1}{3} - \frac{1}{x} = \frac{1}{3.5} \)

\( \Large \frac{1}{x} = \frac{1}{3} - \frac{1}{3.5} \)

\( \Large \frac{1}{x} = \frac{1}{3} - \frac{10}{35} \)

\( \Large \frac{1}{x} = \frac{35 - 30}{35 \times 3}\)

x = 21hr

Hence leakage will take 21 hr to empty the tank

Option(a) is correct

2). A train takes 10 seconds to cross a pole and 20 seconds to cross a platform of length 200 m. What is the length of the train?

A). 50 m

B). 100 m

C). 150 m

D). 200 m

View Answer

Correct Answer: 200 m

Let 'L' be the length of train

A train takes 10 sec to cross a pole \( \Large S_{T} = \frac{L}{10} \)... (i)

and same train takes 20 sec to cross a platform of length 200 m

\( \Large S_{T} = \frac{L+200}{20} \)...(ii)

Solving equation (i) and (ii) we get

\( \Large \frac{L}{10} = \frac{L + 200}{20} \)

2L = L + 200

L = 200m

Hence length of train is 200 m

Option (D)is correct

3). A, B and C can do a piece of work individually in 8, 12 and 15 days respectively. A and B start working together but A quits alter working for 2 days. After this, C joins and works till completion of the work. In how many days will the work be completed?

A). \( 3\)\( \Large \frac{8}{9} \)

B). \( 5\)\( \Large \frac{8}{9} \)

C). \( 5\)\( \Large \frac{2}{3} \)

D). \( 6\)\( \Large \frac{1}{18} \)

View Answer

Correct Answer: \( 3\)\( \Large \frac{8}{9} \)

Total work done by A and B in 2 days = 50 unit

Hence total work left are 2 days = 120 50 = 70 unit

Now C joins with B,

1 day work of (B + C)= 18 unit

70 unit of remaining work will be completed in \( \Large \frac{78}{10} \) day = \( \Large \frac{35}{9} \) day = \( \Large 3 \frac{8}{9} \) day

Hence total number of days = \( \Large 2 + 3 \frac{8}{9} \) = \( \Large 5 \frac{8}{9} \) days

Option (A)is correct

4). The distance between two points (A and B)is 110 km. X starts running from point A at a speed of 60 km/hr and Y starts running from point B at a speed of 40 km/hr at the same time. They meet at a point C, somewhere on the line AB.What is the ratio of AC to BC ?

A). 3:02

B). 2:03

C). 3:04

D). 4:03

View Answer

5). A is thrice as efficient as B and hence completes a work in 40 days less than the number of days taken by B. What will he the number of days taken by both of them when working together?

A). 22.5 days

B). 15 days

C). 20 days

D). 18 days

View Answer

Correct Answer: 15 days

A is thrice efficient as B

Let total unit of work to be done is x unit

Now according to question

\( \Large \frac{x}{3} = x - 40 \)

x = 3x - 120

2x = 120

x = 60

Number of days taken by both of them to 60 complete the work = \( \Large \frac{60}{4} \)= 15 days

6). If 10 persons can dig 8 feet trench in 12 days,then how many days will 8 persons take to dig 6 feet trench?

A). 10 days

B). 10.25 days

C). 11 days

D). 11.25 days

View Answer

Correct Answer: 11.25 days

According to Man-day-work concept

\( \Large \frac{M_{1} \times D_{1}}{W_{1}} = \frac{M_{2} \times D_{2}}{W_{2}}\)

\( \Large \frac{10 \times 12}{8} = \frac{8 \times D_{2}}{6} \)

\( \Large D_{2} = \frac{10 \times 12 \times 6 }{64} \)

= 11.25 days

Option (D)is correct.

7). The height of a tree varies as the square root of its age (between 5 to 17 years). When the age of the tree is 9 years, its height is 4 feet. What will he the height of the tree at the age of 16 years?

A). 5 feet 4 inches

B). 5 feet 5 inches

C). 4 feet 4 inches

D). 4 feet 5 inches

View Answer

Correct Answer: 5 feet 4 inches

Height of the tree varies as square root of its age

\( \Large H \propto \sqrt{A} \)

\( \Large H = K\sqrt{A} \) ... (i)

Putting the value of A and H in equation (i) we get

\( \Large 4 = K\sqrt{9} \)

4 = K(3)

\( \Large K = \frac{4}{3} \)

\( \Large H = \frac{4}{3}\sqrt{A} \)

the original equation

Height of tree at age of 16 years

=\( \Large \frac{4}{3}\sqrt{13} = \frac{16}{3} feet \)

= 5 feet 4 inches

8). The ratio of ages of A and B is 2 : 5 and the ratio of ages B and C is 3 : 4. What is the ratio of ages of A, B and C?

A). 6:15:20

B). 8:05:03

C). 6:05:04

D). 2:15:04

View Answer

9). When an article is sold at 20% discount, the selling price is Rs 24. What will be the selling price when the discount is 30%? (

A). Rs.25

B). Rs.23

C). Rs.21

D). Rs.20

View Answer

Correct Answer: Rs.21

Let the C.P. of article be Rs. 100

Now discount of 20% is given on C.P

SP = Rs. 80

Now here SP = Rs. 24

C.P. of an article = Rs \( \Large \left(\frac{24 \times 100}{80} \right) \) = Rs. 30

Now 30% discount is given original C.P. of an article

SP of article = Rs.(30 -9) = Rs 21

10). A shopkeeper sells his articles at their cost price but uses a faulty balance which reads 1000 g for 800 g. What is his actual profit percentage.

A). 25%

B). 20%

C). 40%

D). 30%

View Answer

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