Quants

The ratio of present ages of A and B is 2 : 3. 6 years hence, the ratio of their ages will be 13 : 18. Find 2/5th of B’s age.

Explanation:

 Let the present ages of A and B are 2x and 3x 

After 6 years, 2x+6 / 3x+6 = 13/18 

Solve, x = 10 B’s age = 30, 

2/5 * 30 = 12

A and B started a business by investing Rs 20,000 and Rs 30,000 respectively. After 8 months both A and B withdraw their money and C joins the business with Rs 40,000. Find the share of A from a profit of Rs 55,300 after a year.

Explanation: 

A’s share : B’s share : C’s share 

20,000*8 : 30,000*8 : 40,000*4 

2 : 3 : 2 

A’s share = 2/(2+3+2) * 55300 = 15,800

The average of 11 results is 50. If the average of first six results is 49 and that of last six is 52, find the sixth result. 

Explanation:

 Total of 11 results = 11*50 = 550 

Total of first six results = 6*49 = 294 

Total of last six results = 6*52 = 312 

So 6th result will be (294+312) – (550) = 56

A certain sum of money amounts to Rs 756 in 2 yrs and to Rs 873 in 3.5 yrs. Find the sum and the rate of interest. 

Explanation: 

SI for 1.5 yrs = 873 – 756 = Rs 117

 So, for 2 yrs SI = 117/1.5 * 2 = Rs 156

Amount for 2 yrs is 756, so P = 756 – 156 = Rs 600 

This gives, r = 100*156/600*2 = 13%

In an alloy weighing 5 kg, 1/3rd is brass and the rest is copper. It is mixed with an alloy weighing 2 kg in which 1/4th is brass and the rest is copper. What is the ratio of brass to copper in the final mixture? 

Explanation:

 After mixing the two, quantity of brass = 1/3 * 5 + 1/4 * 2 = 13/6 

Quantity of copper = 2/3 * 5 + 3/4 * 2 = 29/6

 Ratio of brass to copper = 13/6 : 29/6 = 13 : 29

5 men or 6 women do a piece of work in 61 days. In how many will 6 men and 5 women complete the same work? 

Explanation: 

For these type of questions, 

we have a direct formula as: Days 6m and 5w take = 61*5*6/(5*5 + 6*6) = 30 days In the numerator – days multiplied by number of men women in ‘or’.

 In the denominator we have cross multiplied the number of men with number of women

A bag contains 3 white balls, 5 black balls and 4 yellow balls. 3 balls are drawn at random. What is the probability that at least 1 ball is black in color?

Explanation: 

For at least 1 black, we can have prob = 1 – none is black None is black means 3 balls from 7 balls (3 w + 4 y), ways are 7C3 = 7*6*5/3*2*1 = 35 

There are a total of 12 balls. Ways for drawing 3 balls is 12C3 = 12*11*10/3*2*1 = 220 

So prob. of none black = 7C3 / 12C3 = 35/220 = 7/44

So prob. of at least 1 black = 1 – 7/44 = 37/44

A dealer sold an article at a loss of 2.5%. Had he sold it for Rs 100 more, he would have gained 7.5%. For what value should he sell it in order to have a profit of 12 1/2%?

Explanation: 

We have a direct formula for these questions: CP = More gain*100 / diff in profit %

So here CP = 100*100/(7.5 – (-2.5)) = 100*100/10 = Rs 1000 

So after profit of 12 ½ % or 12.5%, 

SP = (100+12.5)/100 * 1000 = Rs 1125

A boat goes in a river flowing at 1.5 km/hr. The ratio of the times taken by the boat to go downstream and back upstream is 3 : 4. Find the downstream speed.

Explanation: 

Upstream time = 4x, downstream time = 3x R = 1.5

 So using the formula, B = [tu + td] / [tu – td] * R 

Speed of boat in still water, B = [4x+3x/(4x-3x)] * 1.5 = 10.5 km/hr

 So downstream speed = 10.5 + 1.5 = 12 km/hr