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An employer reduces the number of employees in the ratio 8 : 5 and increases their wages in the ratio 7 : 9. As a result, the overall wages bill is
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
The ratio of ages of father and son is 7 : 2. Five years ago the product of their ages was 150. What is the age of the father?
Let father's age = 7x years and son's age = 2x years
According to ques, => (7x − 5)(2x − 5) = 150
=> 14x^{2 }− 35x − 10x + 25 − 150 = 0
=> 14x^{2} − 45x − 125 = 0
=> 14x^{2} − 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)
The sum of the ages of husband and wife at present is 56. Ten years ago the product of their ages was 320. What is the age of the husband and the wife?
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 − x^{2 }− 460 + 10x = 320
=> x^{2 }− 56x + 780 = 0
=> x^{2} − 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 and Elan are working on an Assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take working together on two different computers to type an assignment of 110 pages?
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.
The ratio of present ages of Ramya and Saurabh is 8 : 7. After 10 years the ratio of their ages will be 12 : 11. What is Ramya's present age?
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
If 5x + 9y = 5 and 125x^{3} + 729y^{3} = 120 then the value of the product of x and y is
Expression: 5x + 9y = 5
Cubing both sides, we get:
=> (5x + 9y)^{3} = 125
=> 125x^{3} + 729y^{3 }+ 135xy(5x + 9y) = 125
=> 125x^{3} + 729y^{3} + 135xy ∗ 5 = 125
Since, 125x^{3} + 729y^{3} = 120
on squaring both sides
x^{2} − 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.
If m  5n = 2, then the value of (m^{3} − 125n^{3}  30 mn) is
Using the formula, (x − y)^{3} = x^{3} − y^{3} − 3xy(x − y)
=> (m − 5n)^{3} = m^{3} − 125n^{3} − 15mn(m − 5n)
=> 23 = m^{3 }− 125n^{3} − 15mn ∗ 2
=> m^{3 }− 125n^{3 }− 30mn = 8
Which of the following statement (s) is / are TRUE?
L.H.S. = 26 + 2.6 + 0.26 = 28.86 ≠ R.H.S.
Thus, only II is correct.
=> Ans  (B)
The 4th term of an arithmetic progression is 15, 15th term is 29, ﬁnd the 10th term?
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, A_{4} = a + (4  1)d = 15
=> a + 3d = 15 (i)
Similarly, 15th term, A_{15} = 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, A_{10} = 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)
If the cost price of 15 articles is equal to the selling price of 12 articles, find gain %
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
A man bought an article listed at Rs. 1500 with a discount of 20% offered on the list price. What additional discount must be offered to man to bring the net price to Rs. 1,104?
After having 20% discount price will be =
So for net price of 1104 discount should be 1200  1104 = 96
A is 50% as efficient as B. C does half of the work done by A and B together. If C alone does the work in 20 days, then A, B and C together can do the work in
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.
A man sold 20 apples for Rs. 1000 and gained 20%. How many apples did he buy for Rs. 1000?
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
A grain dealer cheats to the extent of 10% while buying as well as selling by using false weights. His total profit percentage is:
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
What is the equation of the line whose yintercept is 3/4 and making an angle of 45° with the positive xaxis?
Slope of line making an angle of 45° with the positive xaxis = tan(45°)
=> Slope, m = 1
yintercept, 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)
In what ratio is the segment joining (1, 12) and (3, 4) divided by the xaxis?
Using section formula, the coordinates of point that divides line joining A = (x_{1}, y_{1}) and B = (x_{2}, y_{2}) in the ratio a : b
Let the ratio in which the segment joining (1,12) and (3,4) divided by the xaxis = k : 1
Since, the line segment is divided by xaxis, thus ycoordinate 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)
Find equation of the perpendicular bisector of segment joining the points (2, 5) and (0, 7)?
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 (x_{1}, y_{1}) and having slope mm is (y − y_{1}) = m(x − x_{1})
∴ Equation of line l
=> (y  1) = 1/6(x − 1)
=> 6y  6 = x  1
=> x  6y = 1  6 = 5
=> Ans  (C)
Find k, if the line 2x  3y = 11 is perpendicular to the line 3x + ky = 4?
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)
The point P(4, 1) divides the segment joining the points (x, 0) and (0, y) in the ratio 3 : 2. Find x and y?
Using section formula, the coordinates of point that divides line joining A = (x_{1}, y_{1}) and B = (x_{2}, y_{2}) 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)
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