Numerical Ability Quiz

Rice is bought at the rate of Rs 8 per kg. Out of the total quantity of 110 kg, 60 kg of rice is sold at 10% profit. At what rate per kg the remaining need rice need to be sold so that there is a profit of 20% on the total price?

Explanation:
Let remaining (110-60) = 50 kg at x%. So by allegation method,
(60 kg)…………………(50 kg)
10% …………………….x%
…………….20%
(x-20)…………..………10
So (x-20)/10 = 60 kg/50 kg
Solve, x = 32%
50 kg costs = 50*8 = Rs 400
So at 32% profit SP of 50 kg is (132/100) * 400 = Rs 528
So SP of 1 kg = 528/50 = 10.56

In an application form, a candidate mistakenly filled his age 20% more than his actual age. If his actual age is 25, by how much percent the candidate have to reduce his height in order to get the correct age?

Explanation: 100      20

                        25       !                       =25*20/100=5

                                                       =25+5=30 years

Now, we reduce the height so

                           30     25

                            100    !                  = 100*25/30=83.33   So, reduce  16.17%    

         

A, B and C invested Rs 2000, Rs 2500 and Rs 3000 respectively in a business. After 8 months, all withdrew Rs 500 from their investments for only 2 months and then reinvested. Out of a total profit of Rs 66,000 after a year, what is the share of B in the profit?

Explanation:
A invested 2000 for total 10 months (first 8 months and last 2 months) and 1500 for 2 months (9th and 10th month).

 Similarly with others. So A: B: C is
2000*10+1,500*2: 2500*10 +2,000*2 : 3000*10 +2,500*2
23 : 29 : 35
So B gets = [29/(23+29+35)] * 66,000 = (29/87) * 66,000 = 66000/3 = 22000

A, B and C can alone complete a work in 20, 24 and 30 days respectively. They started the work and B left the work 3 days before completion. How much of the total work did B did?

Explanation:
Let work completed in x days, so A and C worked for all x days, and B for (x-3) days. So
(1/20 + 1/30)*x + (1/24)*(x-3) = 1
(1/12)*x + (1/24)*(x-3) = 1
x/12 + x/24 = 1 + 1/8
Solve, x = 9 days
So worked for (9-3) = 6 days
In 6 days, B did 6/24 = 1/4 of work

A box contains 3 blue, 5 green and 4 red balls. If two balls are drawn at random, what is the probability that no ball is green in color?

Explanation:
Total balls = 12
Not green means 2 balls from blue or red color i.e. any of (3+4) = 7 balls
So prob. = ⁷C₂ / ¹²C₂  

              = 7*6/2*1=21

                 12*11/2*1=66

               =7/22       

The average age of A, B and C is 87. If the average age of A and C is 85.5 and that of B and C is 90.5, find the age of C.

Explanation:
A+B+C = 3*87 = 261
A+C = 2*85.5 = 171
B+C = 2*90.5 = 181
Now A+B+C = 261
B + 171 = 261 , so B = 90
C = 181 – 90 = 91

The metal to be used for covering a cylinder having external radius 5 cm, height 21 cm and thickness 1 cm is to be cast from a cylinder. What should be the height of the cylinder of radius 3 cm from which this casting can be done?

Explanation:
Volume of metal to be casted = (22/7)*[(5)² – (4)²]*21
So (22/7)*3²*h = (22/7)*[(5)² – (4)²]*21
Solve, h = 21

A certain sum of money invested at 5% for 6 years yields Rs 630 as simple interest. At what rate of interest the same amount can be received on the same sum after 10 years?

Explanation:
P*5*6/100 = 630
P = 2100
So 2100*r*10/100 = 630
Solve, r = 3%

Three friends A, B and C divide Rs 2400 among them in the ratio 4 : 3 : 5 respectively. If to each of their shares Rs 400 is added, what will be the new ratio of dividing the total money among them?

Explanation:
A got = [4/(4+3+5)] * 2400 = 800, B got = [3/(4+3+5)] * 2400 = 600, C got = [5/(4+3+5)] * 2400 = 1000
When 400 is added to their shares, A gets=800+400 = 1200, B = 1000, C =1400
So new ratio is 1200 : 1000 : 1400 =6:5:7

The sum of the present ages of Ravi and Shikha is 100. Also after 4 years, Ravi’s age will be thrice of Shikha’s. What is the difference in their ages?

Explanation:
Ravi = x, Shikha = 100-x
After 4 years, (x+4) = 3 [(100-x) + 4]
Solve, x = 77 = Ravi’s age
So Shikha’s = 100-77 = 23
Difference in their ages = 77 – 23 = 54

In how many ways all the letters of the word ‘LAYOUT’ be arranged such that all vowels are together?

Explanation: 
Take vowels in a box together as one – AOU, other are L, Y, T
So there are 4 that to be placed for this 4!, now inside the box having vowels are 3letters their arrangement is 3!
So total = 4!*3!=144

An article is marked 20% above the cost price with marked price being Rs 864. The profit gets increased by Rs 108, when the selling price of this article is increased by 10%. What is the original selling price of the article?

 

Explanation:
MP = 864, Also given MP = (120/100)*CP, so CP = Rs 720
Now SP – 720 = Profit(P)
Now given that, when SP increased by 10%, CP is same and profir increased by 108 i.e. becomes P+108, so
(110/100)*SP – 720 = P + 108
Put P = SP – 720 in it
(110/100)*SP – 720 = SP – 720 + 108
(11/10)*SP – SP = 720 – 720 + 108
SP/10 = 108=1080

24% of 750 + 14.2 * 2.5 + 20.2 * 0.5 =

Explanation: 
24% of 750 + 14.2 * 2.5 + 20.2 * 0.5
180 + 35.5 + 10.1=225.6

 (3/4) + (2/3) + (1 1/3) + (2 2/3) =

Explanation: 
(3/4) + (2/3) + (1 1/3) + (2 2/3)
(3/4) + (2/3) + (4/3) + (8/3)
(3/4) + (14/3) = (9+56)/12=65/12

How many words of 4 letters can be formed with the letters of word ‘ACTIVE’ when no letter can repeat in the word?

Explanation:
ACTIVE is 6 letters
Since no letter to be repeated, 6 choices for 1st letter, 5 for 2nd, 4 for 3rd and 3 for 4th
6*5*4*3=360