Quantitative Aptitude - Test 11 - SSC CGL MCQ

Let's say employees were change from 8x to 5x and wage per employee is changed from 7y to 9y
Hence total wage is changed from 56xy to 45xy or in a ratio of 56 : 45

Let father's age = 7x years and son's age = 2x years

According to ques, => (7x − 5)(2x − 5) = 150

=> 14x² − 35x − 10x + 25 − 150 = 0

=> 14x² − 45x − 125 = 0

=> 14x² − 70x + 25x − 125 = 0

=> 14x(x − 5) + 25(x − 5) = 0

=> (x − 5)(14x + 25) = 0

Since, age can't be negative, thus x = 5

∴ Father's age = 7 × 5 = 35 years

=> Ans - (C)

Let husband's age = xx years

=> Wife's age = (56 − x) years

According to ques, (x − 10)(56 − x − 10) = 320

=> (x − 10)(46 − x) = 320

=> 46x − x² − 460 + 10x = 320

=> x² − 56x + 780 = 0

=> x² − 30x − 26x + 780 = 0

=> x(x − 30) − 26(x − 30) = 0

=> (x − 30)(x − 26) = 0

=> x = 30, 26

∴ Ages of the husband and the wife = 30 and 26 years.

Ronald takes 6 hours to type 32 pages

no.of pages typed by ronald per hour = 32/6 = 16/3

 Elan takes 5 hours to type 40 pages

no.of pages typed by elan per hour = 40/5 = 8

in 1hr, both can type 8 + 16/3 pages = 40/3

time taken by both to type 110 pages = 110/(40/3) = 33/4 = 8hrs 15mins    (∵ 1/4 hr = 15mins)

so the answer is option C.

Let Ramya's present age = 8x years and Saurabh's present age = 7x years

According to ques,

=> 88x + 110 = 84x + 120

=> 88x - 84x = 120 - 110 = 10

=> x = 10/4 ​= 2.5

∴ Ramya's age = 8 × 2.5 = 20 years

=> Ans - (A)

It is given that 
it is possible only when a = -1
hence a + 2 = 1
and so

Expression: 5x + 9y = 5

Cubing both sides, we get:

=> (5x + 9y)³ = 125

=> 125x³ + 729y³ + 135xy(5x + 9y) = 125

=> 125x³ + 729y³ + 135xy ∗ 5 = 125

Since, 125x³ + 729y³ = 120

on squaring both sides

x² − x − 6 = 0

x = 3 , x = -2

here -2 will be rejected as square root can not give negative value and hence x = 3

x = 2 + √3​

1/x ​= 2 − √3​

so the answer is option B.

Using the formula, (x − y)³ = x³ − y³ − 3xy(x − y)

=> (m − 5n)³ = m³ − 125n³ − 15mn(m − 5n)

=> 23 = m³ − 125n³ − 15mn ∗ 2

=> m³ − 125n³ − 30mn = 8

L.H.S. = 26 + 2.6 + 0.26 = 28.86 ≠ R.H.S.

Thus, only II is correct.

=> Ans - (B)

The n^th term of an A.P. = a + (n - 1)d, where 'a' is the first term, 'n' is the number of terms and 'd' is the common difference.

4th term, A₄ = a + (4 - 1)d = 15

=> a + 3d = 15 -----------------(i)

Similarly, 15th term, A₁₅ = a + 14d = -29 ------------------(ii)

Subtracting equation (i) from (ii), we get :

=> (14d - 3d) = -29 - 15

=> d = -44/11 ​= −4

Substituting it in equation (i), => a - 12 = 15

=> a = 15 + 12 = 27

∴ 10th term, A₁₀ = a + (10 - 1)d

= 27 + (9× − 4) = 27 − 36 = −9

=> Ans - (D)

Expression: 4x = 7√1024

=> Ans - (A)

Expression:

=> Ans - (B)

Expression: 

= 8 + 13 + 6 + 15 = 42

=> Ans - (C)

Let's say cost price of 15 articles is xx
cost price of 12 articles will be = 12x​/15
selling price of 15 articles is = x
gain = 3x​/15

After having 20% discount price will be =
So for net price of 1104 discount should be 1200 - 1104 = 96

C does 1/20​ amount of work in a day.
And A + B do twice of work as much done by C or A + B = 2C or 2/20​.
So A + B + C together will do amount of work in a day.
And complete work will be done in 20/3​ days.

Selling price of 20 apples = 1000
gain = 20% 
Cost price of 20 will be = 
So on cost price of 1000 amount of apples will be 

Let the retailer buys 110 gram in Rs 100 because of 10 % cheating 

so cost price = 1 gram = Rs 100/110 = Rs 0.909

and retailer sells 90 gram in Rs 100 

and hence selling price = Rs 100/90 = Rs 1.111

Slope of line making an angle of 45° with the positive x­-axis = tan(45°)

=> Slope, m = 1

y-intercept, c = 3/43​

Equation of line having slope mm and y intercept cc is: y = mx + c

=> y = x + 43​

=> 4y = 4x + 3

=> 4x − 4y = −3

=> Ans - (B)

Using section formula, the coordinates of point that divides line joining A = (x₁​, y₁​) and B = (x₂​, y_2​) in the ratio a : b

Let the ratio in which the segment joining (-1,-12) and (3,4) divided by the x-axis = k : 1

Since, the line segment is divided by x-axis, thus y-coordinate of the point will be zero, let the point of intersection = (x, 0)

Now, point P (x, 0) divides (-1, -12) and (3, 4) in ratio = k : 1

=> 4k - 12 = 0

=> k = 12​/4 = 3

∴ Required ratio = 3 : 1

=> Ans - (C)

Let line l perpendicularly bisects line joining  A(2, -5) and B(0, 7) at C, thus C is the mid point of AB.

=> Coordinates of C = 

Now, slope of AB 

Let slope of line l = m

Product of slopes of two perpendicular lines = -1

=> m × −6 = −1

=> m = 1/61

Equation of a line passing through point (x₁​, y₁​) and having slope mm is (y − y₁​) = m(x − x₁​)

∴ Equation of line l

=> (y - 1) = 1/6​(x − 1)

=> 6y - 6 = x - 1

=> x - 6y = 1 - 6 = -5

=> Ans - (C)

Slope of line 2x - ­3y = 11 is
= 2/3
Slope of line 3x + ky = ­4 is −3​/k

Also, product of slopes of two perpendicular lines is -1

=> k = −2 × −1 = 2

=> Ans - (D)

Using section formula, the coordinates of point that divides line joining A = (x₁​, y_1​) and B = (x_2​, y₂​) in the ratio a : b

Now, point P (-4, 1) divides (x, 0) and (0, y) in ratio = 3 : 2

=> 3y = 5 => y = 5/3

=> Ans - (A)