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20 men can complete a work in 12 days and 25 women can complete the same work in 20 days. 12 men and 15 women started the work. After working for some days, they were replaced by 8 men and 10 women who complete the remaining work in 15 days. How much work was completed by initially employed men and women?

Correct

Explanation:
20 m in 12 days so 8 men in (20*12)/8 = 30 days
25 w in 20 days so 10 women in (25*20)/10 = 50 days
So (1/30 + 1/50)*15 = 4/5
So 1 – 4/5 = 1/5 work was done by 12 men and 15 women

Incorrect

Explanation:
20 m in 12 days so 8 men in (20*12)/8 = 30 days
25 w in 20 days so 10 women in (25*20)/10 = 50 days
So (1/30 + 1/50)*15 = 4/5
So 1 – 4/5 = 1/5 work was done by 12 men and 15 women

Question 3 of 10

3. Question

1 points

Category: Quantitative Aptitude

If (tan ɸ + cot ɸ)/ (tan ɸ – cot ɸ) = 2, then find the value of sin ɸ. (0 ≤ ɸ ≤ 90)

Correct

Explanation:
Do componendo and dividend
(tan ɸ + cot ɸ + tan ɸ – cot ɸ)/ (tan ɸ + cot ɸ – (tan ɸ – cot ɸ)) = (2+1)/(2-1)
Gives 2 tan ɸ/2 cot ɸ = 3
Solve, (sin ɸ/cos ɸ) * (cos ɸ/sin ɸ) = 3
So sin^{2} ɸ = 3cos^{2} ɸ
Or sin^{2} ɸ = 3 ( 1 – sin^{2} ɸ)
Or 4 sin^{2} ɸ = 3
Gives sin^{2} ɸ = 3/4
So sin ɸ = √3/2

Incorrect

Explanation:
Do componendo and dividend
(tan ɸ + cot ɸ + tan ɸ – cot ɸ)/ (tan ɸ + cot ɸ – (tan ɸ – cot ɸ)) = (2+1)/(2-1)
Gives 2 tan ɸ/2 cot ɸ = 3
Solve, (sin ɸ/cos ɸ) * (cos ɸ/sin ɸ) = 3
So sin^{2} ɸ = 3cos^{2} ɸ
Or sin^{2} ɸ = 3 ( 1 – sin^{2} ɸ)
Or 4 sin^{2} ɸ = 3
Gives sin^{2} ɸ = 3/4
So sin ɸ = √3/2

Question 4 of 10

4. Question

1 points

Category: Quantitative Aptitude

The angles of elevation of the top of a building and the top of the chimney on the roof of eth building from a point on the ground are x and 45 degree respectively. The height of the building is h metre. Find the height of the chimney in metre.

Correct

Explanation:

AB = h, let AD = y = chimney height
In ∆BCD, tan 45 = BD/BC
So 1 = (h+y)/BC, or BC = h+y
In ∆ABC, tan x = AB/BC
SO tan x = h/BC, so BC = h cot x
Solve both equations, y = h cot x – h

Incorrect

Explanation:

AB = h, let AD = y = chimney height
In ∆BCD, tan 45 = BD/BC
So 1 = (h+y)/BC, or BC = h+y
In ∆ABC, tan x = AB/BC
SO tan x = h/BC, so BC = h cot x
Solve both equations, y = h cot x – h

Question 5 of 10

5. Question

1 points

Category: Quantitative Aptitude

Find the smallest number of 4 digits which is exactly divisible by 9, 12, 15 and 18.

Correct

Explanation:
Least 4 digit number = 1000
LCM of (9, 12, 15, 18) = 180
On dividing 10000 by 180, leaves remainder = 100
So answer = 1000 + (180 – 100)

Incorrect

Explanation:
Least 4 digit number = 1000
LCM of (9, 12, 15, 18) = 180
On dividing 10000 by 180, leaves remainder = 100
So answer = 1000 + (180 – 100)

Question 6 of 10

6. Question

1 points

Category: Quantitative Aptitude

Among the equations: 3x – 2y + 5 = 0; 2x – 3y + 5 = 0; 4x – 3y – 9 = 0; 2x + 9y = 0, the equation of the straight line passing through point (2, 3) is

Correct

Explanation:
Only equation 2x – 3y + 5 = 0 satisfies the point (2,3), so it passes through point (2,3)

Incorrect

Explanation:
Only equation 2x – 3y + 5 = 0 satisfies the point (2,3), so it passes through point (2,3)

Question 7 of 10

7. Question

1 points

Category: Quantitative Aptitude

I is the incentre of ∆ABC. If angle ABC = 80 degrees and angle ACB = 60 degrees, find the value of angle BIC in degrees.

The fourth proportional to (x^{4}– y^{4}), (x^{2} + y^{2}) and (x-y) is

Correct

Explanation:
The fourth proportional of a, band c is bc/a
So fourth proportional = (x^{2} + y^{2}) (x-y)/ (x^{4}– y^{4})
= 1/(x+y)

Incorrect

Explanation:
The fourth proportional of a, band c is bc/a
So fourth proportional = (x^{2} + y^{2}) (x-y)/ (x^{4}– y^{4})
= 1/(x+y)

Question 9 of 10

9. Question

1 points

Category: Quantitative Aptitude

A and B started a business with Rs 2000 and Rs 2500 respectively. After 4 months C also joined with Rs 3000. After further 4 months, A and B withdrew Rs 500 each. If at the end of year C received Rs 7200 as his share from the total profit, then what is the total profit?

What is the arithmetic mean of first 99 even natural numbers?

Correct

Explanation:
First even natural number is 2, and 99th is 198
So we have to find, (2+4+6+….+198)/99 = (99/2) * (2+198)/99
Use the formula to find sum of AP, 1+2+3+4+…+n is (n/2) * (a+l). a is first term, l is last term

Incorrect

Explanation:
First even natural number is 2, and 99th is 198
So we have to find, (2+4+6+….+198)/99 = (99/2) * (2+198)/99
Use the formula to find sum of AP, 1+2+3+4+…+n is (n/2) * (a+l). a is first term, l is last term