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**Two articles are bought for Rs 19,500. After this one is sold at a loss of 20% and the other at a profit of 15%. Find the respective cost prices of the two articles, if after selling it is found that the selling price of both the articles is same.**

A. 10,500 and 9,000

B. 11,500 and 8,000

C. 11,000 and 8,500

D. 9,500 and 10,000

E. None of these**B. 11,500 and 8,000**

Explanation:

Let CP of 1st article = x, then of other = 19500 – x

One at loss of 20%, other at 15% gain. SP is same

So, 80/100 * x = 115/100 (19500-x)

80x + 115x = 115*19500

x = 115*19500/195 = 11500**A jar contains 3 red balls, 4 blue balls, and 6 white balls. Find the probability of at least 2 red balls, when 3 balls are drawn at random.**

A. 11/144

B. 31/286

C. 15/132

D. 19/286

E. None of these**B. 31/286**

Explanation:

Case 1 : 2 red balls:

Prob =^{3}C_{2}×^{10}C_{1}/^{13}C_{3}= 15/143.

Case 2 : 3 red balls:

Prob =^{3}C_{3}/^{13}C_{3}= 1/286.

So total prob. = 15/143 + 1/286= 31/286**A and B together can complete the work in 10 days. B and C can complete the same work in 20 days. A works for 5 days and B works for 7 days, and now the remaining work is done by C in 26 days. Find the number of days for which B can alone work to complete the job.**

A. 25

B. 26

C. 30

D. 32

E. None of these**C. 30**

Explanation:

5 times A’s 1 day’s work + 7 times B’s 1 day’s work + 26 times C’s 1 day’s work = 1

Or it can be written as

5 times A’s 1 day’s work + (5 times B’s 1 day’s work+2 times B’s 1 day’s work) + (2 times C’s 1 day’s work+24 times C’s 1 day’s work) = 1

(5 times A’s 1 day’s work + 5 times B’s 1 day’s work) + (2 times B’s 1 day’s work + 2 times C’s 1 day’s work) + 24 times C’s 1 day’s work) = 1

5 (A+B)’s work + 2 (B+C)’s work + 24 C’s work = 1

5 * 1/10 + 2 * 1/20 + 24 * 1/C = 1

Solve, C = 60 days

B and C complete in 20 days. So B’s 1 day’s work is 1/20 – 1/60 = 1/30**Find the number of ways in which the letters of the word COMPLETE be arranged such that all the vowels of the given word are always together.**

A. 2180

B. 2200

C. 2060

D. 2160

E. None of these**D. 2160**

Explanation:

CMPLT OEE

We have to take OEE together, so in all we have 6 letters {C, M, P, L, T, OEE}

Ways for these 6 is 6!

Now for OEE, ways are 3!, and since it contains 2 E’s, so ways are 3!/2!

Total ways = 6! × 3!/2! = 2160**Two articles are bought for Rs 6000. The first one is sold at 10% loss and the other at a gain of 10%. In this whole transaction a gain of Rs 100 is made on the whole. Find the cost price of the article sold at 10% gain is**

A. Rs 3870

B. Rs 3500

C. Rs 2850

D. Rs 4070

E. Rs 4225**B. Rs 3500**

Explanation:

Gain% on the whole = 100/6000 * 100 = 5/3%

By the method of allegation:

-10 10

. 5/3

10 – 5/3 = 25/3 5/3 – (-10) = 35/3

Ratio = 25/3 : 35/3 = 5 : 7

So CP of 2nd article = 7/(5+7) * 6000 = 3500**A 100 litres solution of sugar and water consists of 20% of sugar. The solution is heated and the water evaporates. After this sugar concentration becomes 80% of the total remaining solution. Find the amount of water being evaporated.**

A. 78 litres

B. 60 litres

C. 75 litres

D. 62 litres

E. 64 litres**C. 75 litres**

Explanation:

In 100 litres solution, sugar = 20 l, water = 80 l

Suppose x litres of water evaporated.

So now the solution becomes (100-x) litres and water becomes (80-x) litres.

In this (100-x) litres, 20% is water.

So 20/100 (100-x) = 80-x

Solve, x = 75**A town has a total population 1,20,000. In this town the percentage of males is 55% and the rest are females. If only 48% of the males and 60% of the females are allowed to vote, then find the total number of voters present.**

A. 64,320

B. 64,080

C. 70,000

D. 69,890

E. 62,080**B. 64,080**

Explanation:

Males = 55/100 * 1,20,000 = 50/100 of 1,20,000 + 5/100 of 1,20,000 = 60,000 + 6000 = 66,000

Male voters = 48/100 * 66,000 = 50% of 66,000 – 2% of 66,000 = 33,000 – 1320 = 31680

Females = 1,20,000 – 66,000 = 54,000

Female voters = 60/100 * 54,000 = 32400

Total voters = 31680 + 32400**A man can row 10 km/hr in still water. When the river is running at 4 km/hr, it takes him 5 hrs to row to a place and come back. How far is the place?**

A. 20 km

B. 22 km

C. 21 km

D. 35 km

E. 24 km**C. 21 km**

Explanation:

B is speed of boat in still water, R is speed of stream

Time is total time taken for upstream and downstream

Distance = time * [B^2 – R^2] / 2*B

=5 * [10^2 – 4^2] / 2*10**In a rectangle if its length increases by 25% and the breadth decreases by 20%, then what is the percentage change in the perimeter of the rectangle?**

A. 20%

B. 0%

C. -5%

D. Cannot be determined

E. None of these**D. Cannot be determined**

Explanation:

Perimeter = 2(l+b)

New perimeter = 2(1.25l + 0.80b)

Change in perimeter = 2 [(1.25l – l) – (0.80b – b)] = 2[0.25l + 0.20b] As the values of l and b are not known, change cannot be determined.**The area of a square is 450 cm**^{2}. Find the length of diagonal.

A. 30 cm

B. 44 cm

C. 28 cm

D. 35 cm

E. 32 cm**A. 30 cm**

Explanation:

1/2 d^{2}= 450

d^{2}= 900, d = 30

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