Maths

Distance between point P and Q is 480 km. A train starts from point P at 6:00 AM with 60 km/hr towards Q. Another train starts from point Q towards P at 7:00 AM with 80 km/kr. At what time the trains will meet?

Explanation:

When 2^nd train starts i.e. at 7 AM (1 hr after 6 AM), distance covered by first train is 60 km (i.e. in 1 hr).
Now 2^nd train also starts and distance between them is now (480-60) = 420 km
Both coming in opposite direction, so relative speed = (60+80) = 140 km/hr
So time = 7:00 AM + (420/140) = 7:00 AM +3 hrs = 10:00 AM

A and B started a business by investing Rs 5000 and Rs 6000 respectively. After 4 months C came with investment of Rs 7000 and B withdrew his whole amount. Now after another 4 months, B reinvested the money as before and A withdrew half of his money. If at the end of year the total profit is Rs 22,000, what is the difference between the share of profit that C gets as compared to his investment?

Explanation:
A invested 5000 for 8 months and then 2500 for 4 months. B invested 6000 for initial 4 months and then for last 4 months i.e. for 8 months. C invested 7000 for (12-4)= 8 months.
So A : B : C is
5000*8 + 2500*4 : 6000*8 : 7000*8
50*8 + 25*4 : 60*8 : 70*8
50*2 + 25 : 60*2 : 70*2
10*2 + 5 : 12*2 : 14*2
25 : 24 : 28
So C got = [28/(25+24+28)] * 22,000 = 8000
So xtra money C got is 8000-7000=૧૦૦૦

From a bag containing 7 white and 5 black balls, 2 balls are drawn one by one without replacement. Find the probability that either both balls are white in color or both are different colored?

Explanation:
Case 1: When both white in color: prob. = 7/12 * 6/11 = 7/22 or 7C2/12C2 = 7/22
Case 2: When both different:
7C1 * 5C1/12C2 = 35/66
Now add both cases: prob. = 7/22 + 35/66 = 56/66 = 28/33

Two varieties of rice are mixed in the ratio 5 : 3. The mixture is sold at a profit of 10% for Rs 24.53 per kg. If the value of 1st variety of rice is Rs 20.50 per kg, how much is the cost of the 2nd variety of rice (per kg)?

Explanation:
SP = 24.53, profit = 10%, so CP = (100/110)*24.53 = Rs 22.30
1st rice………………2nd rice
20.50……………………..x
…………….22.30
x-22.30…………………..1.80
So (x – 22.30)/ 1.80 = 5/3
Solve, x = 25.30

An article is sold at a discount of 25% making a profit of 20%. What would have been the profit percent if the article was sold without discount?

Explanation:
Let MP = Rs 100
at 25% discount gives: SP = Rs 75, so Discount = 25
Now profit = 20%
so CP = (100/120) * 75 = 62.5
No discount given means SP = MP = 100
So Profit% when no discount = [100-62.5/62.5]*100=60

Directions : Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question:

• 1.  If the data in statement I alone is sufficient to answer the question.
• 2.  If the data in statement II alone is sufficient to answer the question.
• 3.  If the data either in statement I alone or statement II alone are sufficient to answer the question.
• 4.  If the data given in both I and II together are not sufficient to answer the question.
• 5.  If the data in both the statements I and II together are necessary to answer the question.

What is the two digit number?
I. The number obtained by interchanging the digits of original number is more than the original number by 36.
II. The difference between the digits is 4 and there addition gives 8.

Explanation:
Let number if 10x+y
From I: (10y+x) = (10x+y) + 36
From II: x+y = 8 and x-y = 4 or y-x = 4
If x+y = 8 and x-y = 4 gives x=6 and y=2
If x+y = 8 and y-x = 4 gives x=2 and y=6
Since we don’t know that difference between which digits is 4, cant be determined.

o    If the data given in both I and II together are not sufficient to answer the question.(ans-4)

What is the rate percent per annum?
I. At the end of 2 years, the difference between compound interest and simple interest is Rs 250 on an amount of Rs 35,000
II. Simple interest obtained after 4 years is Rs 5600 on an amount of Rs 20,000

Explanation:
From I: we are not given that whether CI or SI are calculated at same rate or not, so cant be determined.
From II: 20,000*r*4/100 = 5600, so r=7%

If the data in statement II alone is sufficient to answer the question.(ANs-2)

In how many days, A alone can complete the piece of work?
I. A and B together complete twice the work in 12 days.
II. B can complete 1/2 the work in 5 days.

Explanation:
From I: A+B twice work in 12 days, so 1 work in 6 days
From II: B half work in 5 days, so 1 work in 10 days
So from both, 1/A = 1/6 – 1/10

o    If the data in both the statements I and II together are necessary to answer the question.(ans-5)

How many marks did Shikha get in Computers?
I. She got a total of 225 marks in 3 subjects, with marks in the ratio 1 : 1 : 3.
II. She got 45 marks in Science.

Explanation:
From I: we don’t know, that in the ratio which part if of computer.
From II: cant be determined
Also from both, cant be determined since we don’t know in 1 : 1 : 3, which part is what subject.

o    If the data given in both I and II together are not sufficient to answer the question.(ans-4)

Directions : In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answer –

o    1.  If X > Y

o    2.  If X < Y

o    3.  If X ≥ Y

o    4.  If X ≤ Y

o    5.  If X = Y or relation cannot be established

2x² – 9x – 5 = 0, 6y² – 13y + 6 = 0

Explanation:
2x² – 9x – 5 = 0
2x² – 10x + x – 5 = 0
Gives x = -1/2, 5
6y² – 13y + 6 = 0
6y² – 9y – 4y + 6 = 0
Gives y = 2/3, 3/2
Put on number line
-1/2… 2/3 … 3/2 …. 5 If X = Y or relation cannot be established

4x² – 5x – 6 = 0, 3y² – 13y + 14 = 0

Explanation:
4x² – 5x – 6 = 0
4x² – 8x + 3x – 6 = 0
Gives x = -3/4, 2
3y² – 13y + 14 = 0
3y² – 6y – 7y + 14 = 0
Gives y = 2, 7/3
Put on number line
-3/4… 2… 7/3      If X ≤ Y

4x² – x – 3 = 0, 2y² – 11y + 14 = 0

o    Explanation:
4x² – x – 3 = 0
4x² – 4x + 3x – 3 = 0
Gives x = -3/4, 1
2y² – 11y + 14 = 0
2y² – 7y – 4y + 14 = 0
Gives y = 2, 7/2
Put on number line
-3/4… 1… 2… 7/2 If X < Y

2x² – 13x + 18 = 0, 2y² – 3y – 27 = 0

o    1.  If X > Y

o    2.  If X < Y

o    3.  If X ≥ Y

o    4.  If X ≤ Y

o    5.  If X = Y or relation cannot be established

Incorrect

Explanation:
2x² – 13x + 18 = 0
2x² – 4x – 9x + 18 = 0
Gives x = 2, 9/2
2y² – 3y – 27 = 0
2y² + 6y – 9y – 27 = 0
Gives y = -3, 9/2
Put on number line
-3…. 2… 9/2
When x=2, x>y(-3) and x<="" p="" style="box-sizing: border-box;">

If X = Y or relation cannot be established

9x² – 3x – 2 = 0, 3y² + 16y + 5 = 0

Explanation:
9x² – 3x – 2 = 0
9x² + 3x – 6x – 2 = 0
Gives x = -1/3, 2/3
3y² + 16y + 5 = 0
3y² + 15y + y + 5 = 0
Gives y= -5, -1/3          If X ≥ Y
Put on number line
-5…. -1/3… 2/3