Quants

Ratio of A’s age four years ago and B’s age four years ago was 5 : 8. A’s age 6 years after will be 6 less than B’s present age. Find the ratio of the present ages of A and B.
Explanation: 
4 yrs ago, A-4/B-4 = 5/8 8A – 5B = 12
 After 6 yrs, A + 6 = B – 6 
Solve the equations, A = 24, B = 36
So,2:3

A and B invested Rs 8,000 and Rs 9,000 in a business. After 4 months A withraw Rs 400 and B added Rs 400. What is the share of A from the profit of Rs 10,200?
Explanation: 
8000*4 + 7600*8 : 9000*4 + 9400*8 2 zeros get cancelled and 8 can be taken out in common from all terms. 
We are left with 40+76 : 45+94 116 : 139 
Share of A = 116/(116+139) * 10200 = 4640

5 men can complete a piece if work in 6 days. 3 women can complete the same work in 6 days. 2 men started the work and worked for 6 days. After this 6 women joined with them. In how many days the total work will be completed?
Explanation: 
5 m in 6 days . So 2 m in 5*6/2 = 15 days. They work for 6 days. So they complete 1/15 * 6 = 2/5th of the work Now 2 m and 6 women have to complete remaining work ( 1 – 2/5) = 3/5 3 w in 6 days, so 6 w in 3*6/6 = 3 days 2m do in 15 days, 6 w in 3days so (2m + 6w)’s 1 day’s work = 1/15 + 1/3 = 6/15 = 2/5. Let (2m + 6w) complete remaining 3/5 th work in x days. So 2/5 * x = 3/5. x = 3/2 So total no of days to complete the work is 6 + 3/2 = 7 ½ days

The difference between compound interest and simple interest on a sum for 2 yrs at 10% per annum, when the interest is compounded annually is Rs 16. If the interest were compounded half yearly, the difference in two interests would be

Explanation: 

10    100

16     ?

So,160 

Now,160 10% of amount so 100% is 1600

So,2 years simple interest is 320 RS  

Now,Half yearly compound interest is=1600*105/100*105/100*105/100*105/100=1944.81 ,1944.81-1600=344.81

Now,Difference=344.81-320=24.81

In a can, A and B are in the ratio 7 : 5. When 9 litres of mixture is drawn off and 9 litres of B is put in, the ratio of A : B becomes 7 : 9. How many litres of A was contained in the can initially? 
Explanation:
A = 7x litres, B = 5x litres
 After drawing off 9 litres, A left = 7x – 7/12 * 9 = (7x – 21/4) litres, 
B left = 5x – 5/12 * 9 = (5x – 15/4) litres 
After adding 9 litres of B, B becomes (5x – 15/4 + 9) litres 
Now, (7x – 21/4) / (5x – 15/4 + 9) = 7 / 9 Find x, x = 3,
 A contained in can = 7x = 21 litres

A gave 40% of amount to B. From this B gave 20% to C. From remaining B spends 40% on food and 20% of transport. Now he is left with Rs 912. Find the amount received by B.
Explanation:
 Let A has Rs x B gets 40/100 *x = 2/5 * x 
After giving 20% to C, B is left with 80/100 * 2/5 * x = 8/25 * x 
After spending 40% on food and 20% of transport, B left with 40/100 * 8/25 * x which is equal to 912 And we have to find 40/100 * x which equals 912 * 25/8 = 2850
or
 40    912
 100     ?
100*912/40=2280

Now,80     2280
       100     ?
2280*100/80=2850

A bag contains 3 white balls, 5 black balls and 4 yellow balls. 4 balls are drawn at random. What is the probability that there is one ball of each color?
Explanation: 
There are a total of 12 balls. Ways for drawing 4 balls is 12C4= 12*11*10*9/4*3*2*1 = 495 
Case 1 : 2 w balls, 1 b and 1 y Ways are3C2*5C1*4C1=60 
Case 2 : 1 w balls, 2 b and 1 y Ways are 3C1*5C2*4C1=90
 Case 3 : 1 w balls, 1 b and 2 y Ways are 3C1*5C1*4C2=120
 So total number of ways to draw 4 balls, 1 of each color = 60+90+120 = 270 
So required prob. = 270/495 = 6/11
  
A shopkeeper sells 25 articles at Rs 45 per article after giving 10% discount and earns 50% profit. If the discount is not given, the profit gained is?
Explanation:
 Let MP = x SP of 1 article = 90/100 * x = 45, so x = 50 
CP of 1 article = 100/150 * 45 = 30 
If discount not given, SP = MP = 50, CP = 30, Find profit% 662/3

A man covered a certain distance at some speed. Had he moved 3 km/hr faster, he would have taken 40 min less. If he had moved 2 km/hr slower, he would have taken 40 min more. The distance in km is

Explanation:
 For these types of ques, when u r not given actual speed, but given faster and slower speeds, use: Let faster speed = s1 = 3, slower speed = s2 = 2
 Average speed of journey = 2* (s1*s2)/s1-s2 = 2* (3*2) /(3-2) = 12 km/hr
 Now distance = (s+s1) * (s-s2) / (s+s1) – (s-s2) * difference in times Here difference in times is 40 mins more – 40 mins early = 80 min = 80/60 hrs 
So, distance = (12+3) * (12-2) / (12+3) – (12-2) * 80/60 = 40 km