## Sunday, 23 October 2016

### Set A

1.What least number must be subtracted from 5731625, to get a number exactly divisible by 3546?
(a) 1189
(b) 1829
(c) 1289
(d) 1982

2.Find the least number of 5 digits which is exactly divisible by 456.
(a) 10456
(b) 10424
(c) 10032
(d) 10023

3.Find the number which is nearest to 68624 and exactly divisible by 587.
(a) 68679
(b) 69156
(c) 68569
(d) 68689

4.Find the number nearest to 144759 and exactly divisible by 927.
(a) 144906
(b) 144612
(c) 144169
(d) 144621

5.Find the greatest number of 5-digits, which is exactly divisible by 547.
(a) 99456
(b) 99554
(c) 10545
(d) 99545

6.What least number must be added to 954131, to get a number exactly divisible by 548?
(a) 63
(b) 563
(c) 485
(d) 611

7.What least number be subtracted from 6501 to get a number exactly divisible by 135?
(a) 21
(b) 12
(c) 35
(d) 53

8.What least number be added to 5200 to get a number exactly divisible by 180.
(a) 160
(b) 60
(c) 20
(d) 180

9.Find the number which is nearest to 6555 and exactly divisible by 21.
(a) 6558
(b) 6576
(c) 6552
(d) 6534

10.Find the number which is nearest to 8845 and exactly divisible by 80.
(a) 8890
(b) 8810
(c) 8800
(d) 8880

1.c
2.c
3.a
4.b
5.b
6.c
7.a
8.c
9.c
10.d

### Set B

1. The average age of the Indian football team is 30 years. The average age of 5 of the players is 29 years and that of another set of 5 players, totally different from the first five, is 27 years. If it is the captain who was not included in either of these two groups, then find the age of the captain
(a) 75 years
(b) 55 years
(c) 50 years
(d) 58 years

2. 2 men and 4 boys can do a piece of work in 10 days, while 4 men and 5 boys can do it in 6 days. Men and boys are paid wages according to their output. If the daily wage of a man is Rs. 40, then the ratio of daily wages of a man and a boy will be
(a) 5 : 3
(b) 5 : 2
(c) 4 : 7
(d) 7 : 3

3. A person ordered 4 shirts of brand A and some shirts of brand B. The price of one shirt of brand A was twice that of brand B. When the order was executed, it was found that the numbers of the two brands has been interchanged. This increased the bill by 40%. The ratio of the number of brand A shirts to that of brand B shirts in the original order was
(a) 1 : 2
(b) 1 : 3
(c) 1 : 4
(d) 1 : 5

4. If three numbers are in the ratio 1 : 2 : 3 and half the sum is 18, then the ratio of squares of the numbers is:
(a) 6 : 12 : 13
(b) 1 : 2 : 3
(c) 36 : 144 : 324
(d) 3 : 5 : 7

5. Rs. 2250 is divided among three friends Apurva, Jitendra and Rajiv is such a way that 1/6th of Apurva’s share, 1/4 th of Jitendra’s share and 2/5th of Rajiv’s share are equal. Find Apurva’s share.
(a) Rs. 720
(b) Rs. 1080
(c) Rs. 450
(d) Rs. 1240

6. A milkman makes 20% profit by selling milk mixed with water at Rs. 9 per litre. If the cost price of 1 litre pure milk is Rs. 10, then the ratio of milk and water in the said mixture is
(a) 3 : 1
(b) 4 : 1
(c) 3 : 2
(d) 4 : 3

7. A, B and C started a business by investing Rs. 40500, Rs. 45000 and Rs. 60000 respectively. After 6 months C withdrew Rs. 15000 while A invested Rs. 4500 More. In annual profit of Rs. 56100, the share of C will exceed that of A by
(a) Rs. 900
(b) Rs. 1100
(c) Rs. 3000
(d) Rs. 3900

8. The cost of an apple is twice that of a banana and the cost of a banana is 25% less than that of an orange. If the cost of each type of fruit increases by 10%, then the percentage increase in the cost of 4 bananas, 2 apples and 3 orange is
(a) 10%
(b) 12%
(c) 16%
(d) 18%

9. A number is mistakenly divided by 5 instead of being multiplied by 5. Find the percentage change in the result due of this mistake.
(a) 96%
(b) 95%
(c) 2400%
(d) 200%

10. The price of sugar falls by 20%. How much sugar can be bought now with the money that was sufficient to buy 20 kg of rice previously?
(a) 5 kg
(b) 15 kg
(c) 25 kg
(d) 30 kg

Solutions
1. (c); Age of the captain =(11 × 30) – {(5 × 29) + (5 × 27)}
= (330 – 280) yrs.
= 50 yrs.

2. (b); (2m + 4b) × 10 = (4m + 5 b) × b
⇒ 2m = 5 b
So, 5b = 2 × 40
⇒ b = (2 × 40)/5= 16
∴ Required ratio = 40 : 16 = 5 : 2

3. (b);
Let the number of shirt of brand B be x.
Let the cost of a shirt of brand B be Rs. 1
Origianl cost = 4 * 2 + x = Rs. (8 + x)

4x + 2x = (8 + x) * (140/100) = (8 + x) 7/5
⇒ x = 12
∴ Required ratio = 4 : 12 = 1 : 3

4. (c); Half the sum = 18
⇒ total sum = 36
⇒ Nos. will be 6, 12 and 18
So, ratio of squares = 62 : 122 : 182
= 36 : 144 : 324

5. (b); A.T.Q.
A/6 = J/4 = 2/5 R
⇒ A : J : R
= 6 : 4 : 5/2
= 12 : 8 : 5
⇒ Apoorva’s share
=12/(12 + 8 + 5) × 2250 = Rs. 1080

6. (a); S.P. at 20% profit = Rs. 9/litres
⇒ Cost of mixture = 9/120 × 100 = Rs. 7.5 /litre
Now, let the ratio of milk and water in the mixture = x :  y
⇒ ((10 × x) + (0 × y))/(x + y) = 7.5
⇒ 10x = 7.5 (x + y)
⇒ x : y = 3 : 1

7. (d); Ratio of equivalent capitals of A, B and C for 1 month
= (40500 × 6 + 45000 × 6) : (45000 × 12) : (60000 × 6 + 45000 × 6)
= 57 : 60 : 70
Sum of ratios = 57 + 60 + 70 = 187
Required difference = (70 – 57)/187 = 56100
= (13/187) × 56100= Rs. 3900

8. (a); Let the cost price of 1 orange = Rs. 1
∴ C.P. of 1 banana = Rs. 3/4
And C.P. of 1 apple = Rs. 3/2
New prices :
1 oranges = Rs. 1.1
1 banana = 3/4 × 110/100= Rs. 0.825
1 apple = 3/2 × 110/100 = Rs. 1.65
∴ Original price of (4 bananas + 2 apples + 3 oranges)
= Rs. (3 + 3 + 3) = Rs. 9
New price of (4 banana + 2 apples + 3 oranges)
= Rs. (4 × 0.825 + 2 × 1.65 + 3 × 1.1)
= 9.9
Percentage increase = (9.9 – 9)/9 × 100= 10%

9. (a); Let the number be x
⇒ % change
= (original result – changed result)/(original result) × 100%
= (5x – x/5)/5x × 100%
= 96%

10. (c); 20% decrease in price
⇒ 25% increase in consumption (when expenditure is constant)
⇒ increased amount of sugar = 25% of 20 kg = 5 kg
Total amount now of sugar = (20 + 5) kg = 25 kg

### Set C

1. Simmons purchased a refrigerator on the terms that he is required to pay Rs. 1500 cash down payment followed by Rs. 1020 at the end of first year, Rs. 1003 at the end of second year and Rs. 990 at the end of third year. Interest is charged at the rate of 10% per annum compound interest. What is the cash price of the refrigerator?
(a) Rs.  4000                         (b) Rs. 4100
(c) Rs. 4150                          (d) Rs. 4200

2. Alex and Bobin together can complete a work in 12 days. Alex alone can complete in 20 days. If Bobin does the work only half a day daily, then in how many days, Alex and Bobin together will complete the work?
(a) 10 days                           (b) 20 days
(c) 11 days                           (d) 15 days

3. Anand takes 10 days less than the time taken by Bakshi to finish a piece of work. If both Anand and Bakshi can do it in 12 days, then the time taken by Bakshi alone to finish the work is
(a) 30 days                           (b) 27 days
(c) 20 days                           (d) 25 days

4. A takes 5 days more than B to do a certain job and 9 days more than C; A and B together can do the job in the same time as C. How many days A would take to do it ?
(a) 16 days                           (b) 10 days
(c) 15 days                           (d) 20 days

5. A pipe of diameter d can drain a certain water tank in 40 minutes. The time taken by a pipe of diameter 2d for doing the same job in :
(a) 5 minutes                       (b) 10 minutes
(c) 20 minutes                     (d) 80 minutes

6. Two pipes A and B can fill a water tank in 20 and 24 minutes respectively and a third pipe C can empty at the rate of 3 gallons per minute. If A, B and C opened together fill the tank in 15 minutes, the capacity (in gallons) of the tank is:
(a) 180                                 (b) 150
(c) 120                                 (d) 60

7. Two  bullets of shot gun were fired at a place at an interval of 28 minutes 30 seconds. A person approaching the firing point in his car hears the two sounds at an interval of 27 minutes. The speed of sound is 330 m/ sec. What is the speed of the car ?
(a) 44 km/hr                        (b) 66 km/hr
(c) 64 km/hr                        (d) 54 km/hr

8. In a race of 600 metres, Sonu beats Monu by 60 metres and in a race of 500 metres, Monu beats Bablu by 25 metres. By how many metres will Sonu beat Bablu in a 400 metre race ?
(a) 48 m                                (b) 52 m
(c) 56 m                                (d) 58 m

9. Two trains are running on parallel lines in the same direction at speeds of 40 kmph and 20 kmph respectively. The faster train crosses a man in the second trains in 36 seconds. The length of the faster train is
(a) 200 metres                     (b) 185 metres
(c) 225 metres                     (d) 210 metres

10. A boat goes down stream at x km/h and upstream at y km/h. The speed of the boat in still water is
(a) 0.5 (x + y)                       (b) 0.5 (x – y)

(c) x + y                               (d) x – y

Solutions
1. (a); Cash price of refrigerator = 1500 + 1020/1.1 + (1003)/(1.1)2 + 990/(1.1)3
= 1500 + 1020/1.1 + 1003/1.21 + 990/1.331
= 1500 + 2500
= 4000

2. (d); When Bobin works normally then days taken by Bobin to complete the work = (20 × 12)/(20 – 12) days
= 30 days
Now, If Bobin does the work only half a day daily ⇒  Bobin will take twice the total days to complete the whole work alone
⇒ Now No. of days taken by Bobin = (30 × 2) days
= 60 days
So, Now days taken by (Alex + Bobin) together to do the whole work = (20 × 60)/ (20 + 60) = 15 days

3. (a); Let time taken by Bakshi in completing the work = x day
∴ Time taken by Anand (x – 10) days
∴ 1/x + 1/(x – 10) = 1/12
⇒ (x – 4) (x – 30) = 0
⇒ x = 30 because x ≠ 4

4. (c); Let days taken by A to do the whole work = x days
So, days taken by B to do the whole work = (x – 5) days
And, days taken by C to do the whole work = (x – 9) days
According to the question
Days taken by (A + B) together to do the whole work = Days taken by C alone to do the whole work
⇒ (x (x – 5))/(x + (x – 5)) = x – 9
or, (x – 3) (x – 15) = 0
⇒ x = 3 or 15
But x = 3 is not possible as x – 5 or x – 9 will become negative.
So, x = 15 days

5.  (b); Time µ 1/(cross – sectional area of the pipe)
Time µ 1/(π/4 d2)
Time µ 1/d2
So, t2 = t1 (d1/d2)2
t1 = 40 minutes, d1 = d, d2 = 2d
∴ t2 = 40 (d/2d)2
t2 = 40(1/2)2
t2 = 10 minutes
⇒ time taken by a pipe of diameter 2d for doing the same job = 10 minutes

6. (c); Let the capacity of the tank be x gallons.
Quantity of water filled in the tank in 1 minute when all the pipes A, B and C are opened simultaneously = x/20 + x/24 – 3
According to the question, x/20 + x/24 – 3 = x/15
⇒ x = (3 × 120)/3 = 120 gallons

7. (b); Let speed of car = x km/hr.
Here, Distance covered by the car in 27 minutes = Distance covered by the sound in (28 minutes 30 seconds – 27 minutes)
⇒ x km/hr × (27/60) hr.
= (300 × 18/5 km/hr) × (1.5/60 hr)
⇒ x = 66
⇒ Speed of car = 66 km/hr.

8. (d); In the race between Sonu and Monu.
Distance travelled by Sonu and Monu in same time = 600 mtr. & (600 – 60) mtr = 600 mtr. & 540 mtr.
⇒ In the same time,
Ratio of distance travelled by Sonu & Monu = 10 : 9
Similarly,
In the same time, Ratio of distance travelled by Monu & Bablu = 500 : (500 – 25)
= 500 : 475
= 20 : 19
So, In the same time
Ratio of distance travelled by Sonu, Monu & Bablu = 10 × 20 : 9 × 20 : 9 × 19
= 200 : 180 : 171
⇒ When Sonu travels 200 m, Bablu will travel 171 m
So, When Sonu travels 400 m, Bablu will travel 342 m
⇒ In 400 m race between Sonu & Bablu,
Required No. of metres by which Sonu will win the race = 400 m – 342 m
= 58 m

9. (a); Let x = length of the faster train ( in mtr.)
So, 36 seconds = (x + 10)/((40 – 20) kmph)
⇒ x = 36 second × 20 × 5/18  m/sec
= 200 mtr.

10. (a); Speed of boat in still water = (Sdown + Sup)/2
= (x + y)/2 = 0.5 (x + y)