Type Here to Get Search Results !

# SSC MTS 2020| Previous year solved paper| 02-11-2021, 3rd Shift| Educalypse|

## SSC MTS 2020| Exam Date: 02-11-2021, 3rd Shift|

Q1. A retailer bought 250 kg of a cereal and sold it at a profit to the extent of what he paid for 160 kg. What is his profit percentage?

... Ans: b. 64
SP of 250 kg - CP of 250 kg = CP of 160 kg or, SP of 250 kg = CP of 410 kg or, \frac{SP}{CP} = \frac{410}{250} = \frac{41}{25} ] Difference = 16 Profit = \frac{16}{25} × 100 % = 64 %

Q2. The father of a girl is three years older than his mother. Six years ago the average age of the girl and her parents was 32 years, and the age of the father was twice the present age of his daughter. What is the present age (in year) of the mother?

F            M            D

2x            2x-3        x-6       →   -6  → 32×3= 96

2x+6        2x+3          x       →   0   →  96+18= 114

check all options.

For explanation check the video.

Q3. The ratio of two numbers is 4:5. If one is substracted from the first number, and two is added to the second number, then the ratio becomes 3:4, What will be the ratio when eight and four are, respectively, added to the first and the second number?

4x, 5x

\frac{4x-1}{5x+2} = \frac{3}{4}

or, x = 10

\frac{40}{50} = \frac{48}{54} = \frac{8}{9}

Q4. The value of 120 ÷ [ \frac{2}{3} × ( 1 - \frac{2}{5}) × 5] + [ \frac{9}{8} of \frac{4}{3} + \frac{3}{4} of \frac{2}{5}] is?

120 ÷ [ \frac{2}{3} × \frac{3}{5} × 5] + [ \frac{3}{2} × \frac{2}{1}]

= 120 ÷ 2 + 3

= 63

Q5. Study the pie chart and answer the question that follows.

The number of people applying for a passport from a city was monitored, and it was found that the numbers ( in multiple of hundred) during the first five months of 2019 were as follows: January (M1) - 248, February (M2) - 134, March (M3) - 162, April (M4) - 94, May (M5) - 72. These have been represented through the given pie chart.

The number of people in M5 is what percentage (correct up to two decimal places ) of that two months M3 and M4 combined?

\frac{72}{256} × 100

= \frac{900}{32}

= 28.13

Q6. The average of ten numbers is A. If c is substracted from each number, except the tenth, and ( c-1) is substracted from the tenth number, then what will be the new average?

Therefore, A_\alpha = \frac{X - 9c -c +1}{10}

or, A_\alpha = A - c + 0.1

Q7. The total surface area of a hemisphere is very nearly equal to that of an equilateral triangle. The side of the triangle is how many times ( approximately ) of the radius of the hemisphere?

... Answer is d. \left(4\pi\sqrt3\right)^{0.5}

3\mathrm{πr}^2 = \frac{\sqrt3}4a^2

or, a = r\left(4/\sqrt{3}\right)^\frac12

Q8. Two cyclists start simultaneously from two points A and B, their destination being B and A, respectively. After crossing each other, they precisely take 2 hours 33 minutes 36 seconds and 1 hour 26 minutes 24 seconds respectively to reach their destinations. What is the ratio of the speed of the first to that of the second cyclist?

\frac{153\frac{3}{5}}{86\frac{2}{5}} =\frac{768}{432}

Therefore, \frac{B}{A} = \sqrt{\frac{768}{432}} = \sqrt{\frac{16}{9}}

or,   \frac{A}{B} =  \frac{3}{4}

Q9. The fourth proportional of 18, 27, 68 is :

18, 27, 68, x

\frac{18}{27} =  \frac{68}{x}

or, x = 102

Q10. By what percentage is the percentage of the number of vowels in the word CONSONANT less than the percentage of consonants in it?

V = 3

C = 6

Therefore,  \frac{3}{8}× 100 = 50%

Q11. Y takes five days more than X to finish a work. Working together, they finish the work in six days. In how many days can Y finish it working alone?

We can do it by checking options.

Q12. What is the range of the distribution of a variable which takes the ten values:

17, 18, 27, 11, 24, 21, 34, 21, 17, 32, ?

Range = Highest value - Lowest value

So, range = 34-11 = 23

Q13.  Study the pie chart and answer the question that follows.

The number of people applying for a passport from a city was monitored, and it was found that the        numbers ( in multiple of hundred) during the first five months of 2019 were as follows:
January (M1) - 248, February (M2) - 134, March (M3) - 162, April (M4) - 94, May (M5) - 72. These have been represented through the given pie chart.

What is the central angle ( to the nearest ) of the sector corresponding to M1?

\frac{248}{400+290+20} =  \frac{248×360}{710}

Calculate approximately.

Q14.   Study the pie chart and answer the question that follows.

The number of people applying for a passport from a city was monitored, and it was found that the numbers ( in multiple of hundred) during the first five months of 2019 were as follows: January (M1) - 248, February (M2) - 134, March (M3) - 162, April (M4) - 94, May (M5) - 72. These have been represented through the given pie chart.

If the number of people during M2 and M5 had, respectively, been 50% less and 50% more than what has been represented in the pie chart, then what would be the central angle (nearest to degrees) of the sector corresponding to M5?

SOLUTION

Q15. The speed of light is very nearly equal to 3 × 10^17 nanometre per second. How much time ( in seconds), approximately, does it take light to travel from the moon to the earth, the average distance between them being 384000 km? ( 1 nanometre = 10^{-9} metre )

check the video solution.

Q16. When a rectangle is divided into three equal parts, each of them turns out to be a square of area 16 cm^2 . What is the perimeter ( in cm ) of the rectangle ?

Check the video.

Q17. Two inlet pipes can separately fill a cistern completely in 8 hours and 10 hours respectively. They are operated for 2 hours, after which the second pipe is closed, and an outlet pipe which can drain out water from the full cistern in 20 hours is opened. How much time will it take to fill the cistern completely from the instant of opening the outlet pipe?

... Answer is c. 7 hours 20 minutes
A           B             C

8           10            -20

40

5             4               -2

(5+4) × 2 = 18

40 - 18 = 22

\frac{22}{5-2} = \frac{22}{3} = 7\frac{1}{3}

Q18. Simplify the following expression,

... Answer is b. - \frac{23}{6}

\frac{10+\frac{17}{2}-\frac{33}{8}}{\frac{1}{2}\left[\left(\frac{9}{4}+\frac{3}{2}\right)\div\left(-\frac{1}{2}\right)\right]}

=\frac{80+17×4-33}{(9+6)×2}

= -\frac{115}{30}

= -\frac{23}{6}

Q19. The interest, compounded annually, on a sum of ₹ 3240 after two years is ₹370. What is the rate of interest, correct up to two decimal places?

A= P\left(1+\frac{R}{10}\right)^2

\frac{3610}{3240} = \left(1+\frac{R}{10}\right)^2

\frac{10}{18} = R

R = \frac{10}{18}× 100 = 5.56%

Q20. The HCF of two 2-digit numbers is 19 and their sum is 152. What is their difference?

19x, 19y

( x+y) = \frac{152}{19}

x+y = 8

x=3

y=5

19×(5-3) = 38

Q21. A certain sum was invested on simple interest for a period of seven years. During the period of the sixth and the seventh years combined, the interest earned was ₹292. If the maturity amount is ₹3942, then what is the rate percentage of the interest?

check the video

Q22. An article, whose list price was ₹ 720, was subject to two successive discounts of 20% and 10%. What is the amount (in ₹) of discount that a customer would get while purchasing the article?

20 + 10 - \frac{20 × 10}{100}

=28%

720×\frac{28}{100} = \frac{1008}{5} = 201.6

Q23. If a shopkeeper purchases a certain number of items for a certain sum and sells a fraction of the said number for the same amount, then his profit is 300%. What is the fraction?

... Answer is a. \frac{1}{4}

\frac{300}{100} = \frac{3}{1}

CP = 1

SP = 4

Fraction = \frac{1}{4}

Q24. A batswoman missed her century by four runs in an innings, in which the scoring shots in the form of sixes, fours, threes, twos and singles, were in the proportion 1:3:2:7:10. How many runs did she score in singles?

6+12+6+14+10 = 48 × 2 = 96

Therefore, runs scored in singles = 10 × 2= 20

Q25. The area (cm^2) of a sector of a circle of radius 2 cm is \frac{4\pi}{5}. What is the central angle ( in degree ) of the sector?

\frac{4π}{5} = 72