 Important for :
1
In St. Peter’s college Agra an exhibition was organised, hand-made crafts are displayed for sale. Some students are assigned the work of selling crafts. The overall profit p depends on the number of students x selling the crafts on that particular day and is given by the equation p = 250x  5x2. The school manager claims to have made a maximum profit. Find the number of students engaged in selling the crafts and the maximum profit made.
» Explain it
C
For profit to be maximum, the derivative of p with reference to x must be 0 and hence

 = d (250x – 5x2) = 0 = 250 – 10x = 0 dx

So x = 25

Now p for x = 25 is

= 250 (25) – 5 (25)2 = Rs3125

Hence, option (C) is correct.

2
Virat prepares a budget to visit New York. However, he spends 12% of his budget on the first 10% days of his travel when he stays in the city. He knows that he has to spend another 35% of days in city itself, after which he would travel to the country side. What should be the minimum decrease in spending in country side as a percentage of his spending in city so as to complete his travel on the initial budget itself?
» Explain it
B
Budget spent on 10% of days = 12%

 So, in 1% of days = 12 10

 35% remaining days in city = 12 × 35 = 42 10

Overall budget spent on 45% of days in city = 54% Days remaining = 55%, Budget remaining = 46%

 In 1% of day remaining, he can spend = 46 of budget 55

Therefore, % decrease reqd. =
 12 – 46 10 55
× 100 = 30.33%
12
10

Hence, option (B) is correct.

3
Class A has boys to girls in the ratio 2 : 3, Class B has girls to boys in the ratio 5 : 3. If the number of students in Class A is at least twice as many as the number of students in Class B, what is the minimum percentage of boys when both classes are considered together?
» Explain it
C
Let us first rewrite the numbers a touch – 40% of students in Class A are boys, and 37.5% of boys in class B are boys. The overall percentage of boys should lie between these two numbers.

Now, class A has at least twice as many students as class B. So, the overall weighted average should definitely be closer to the percentage of boys in class A, or closer to 40%.

Now, the number of students in class A can be much higher than the number in class B, in which case the overall percentage would practically be 40%. This is the maximum percentage that can be there.

For the minimum percentage, we need to consider the other extreme-where class A has exactly twice as many students as class B.

The weighted average would be

 2 × 40% + 1 × 37.5 = 39.17% 3

Hence, option (C) is correct.

4
Rahul Gandhi borrowed Rs.6240 from Manoj Tiwari on September 1 and promised to repay it by the end of the month. Manoj Tiwari put forth a condition that Rahul Gandhi should repay an amount each day and that the difference between the amounts paid in any two consecutive days should be Rs.10, i.e. the amount to be paid on a particular day (except the first day) should be Rs.10 more than the amount paid on the previous day. How much did she pay Manoj Tiwari on September 1?
» Explain it
E
Let us assume that Rahul Gandhi paid Rs.x to Manoj Tiwari on September 1. As he has to repay the entire money, i.e., Rs.6240 in 30 days and the amounts paid on any day should be Rs.10 more than the amount paid on the previous day,

X + X + 10 + X + 20 + ………. + X + 290 = 6,240

 = 30 (2x + 29 × 10) = 6240 2

30 (2x + 290) = 12480

X = 63

So, Rahul Gandhi paid Rs.63 to Manoj Tiwari on September l.

Hence, option (E) is correct.

5
Life Insurance Company issues semi-prime, prime and most prime policies. Among the company’s policy holders of a certain age, 50% are semi- prime with a probability of 0.01 of dying in the next year, 30% are prime with a probability of 0.008 of dying in the next year and 20% are most prime with a probability of 0.007 of dying the next year. If a policy holder of that age dies in the next year, what is the probability of the deceased being a prime policy holder?
» Explain it
B
The expected number of deaths among all the policy holders of given age (Let X) during next year

 T = { 50 (0.01) + 30 (0.008) + 20 (0.007) } 100 100 100

T = Total no. of policy holder of age X

 = T (0.88) 100

If any of these policy holders (who die during next year) is picked at random, the probability that he is Prime policy holder is
 30 × 0.008 × T 100
=     = 0.2727
24
 0.88 × T 100
88

Hence, option (B) is correct.