TCS Question Bank Quants 7

Find solutions for all the questions at the end of each set:

Set A


1.A cricket player has an average score of 30 runs for 42 innings played by him. In an innings, His highest score exceeds his lowest score by 100 runs. If these two innings are excluded, his average of the remaining 40 innings is 28 runs. His highest score in an innings is
(1)125
(2) 120
(3) 110
(4) 100

2.In a class, the number of girls is 20% more than that of the boys. The strength of the class is 66. If 4 more girls are admitted to the class, the ratio of the number of boys to that of the girls is
(1) 1 : 2
(2) 3 : 4
(3) 1 : 4
(4) 3 : 5 

3.In a certain examination, the number of passes and failures are in the ratio 3 :2 If 12 more students had passed, then the ratio of passes to failures would have been 21 : 10. The number of students who have passed the examination is
(1) 30
(2) 35
(3) 40
(4) 50

4.The difference between compound and simple interests on Rs. 5,000 for two years at the same rate is Rs. 72. The rate of interest per annum is
(1) 15%
(2) 12%
(3) 10%
(4) 8%

5.Rs. 3,903 is to be divided between A and B so that A’ s share at the end of 7 years may be equal to B’s share at the end of 9 years, at 4% per annum compound interest, The present share of B is
(1) Rs. 2,218
(2) Rs. 2,028
(3) Rs. 1,875
(4) Rs. 1,685

6.A sum amounts to Rs. 2,916 in 2 years and to Rs. 3,149.28 in 3 years at same rate of compound interest. The sum is
(1) Rs. 2500
(2) Rs. 2400
(3) Rs. 2250
(4) Rs. 2000

7.A dealer buys an article marked at Rs. 25,000 with successive discounts of 20% and 5%. If he spends Rs. 1,000 on its repairs and sells it for Rs. 25,000, then his gain per cent is 
(1) 20
(2) 25
(3) 30
(4) 35

8.A can complete a piece of work in 36 days, B in 54 days and C in 72 days. All the three began the work together but A left 8 days before the completion of the work and B, 12 days before the completion of the work. Only C worked upto the end. In how many days was the work completed?
(1) 24
(2) 25
(3) 27
(4) 30

9.Two stations X and Y are 900km apart. A train starts from X and moves towards Y at 70km/hr. Another train starts from Y at the same time and moves towards X at 80km/hr. How far from X will they cross each other?
(1) 150km
(2) 300km
(3) 420km
(4) 450km

10.A man buys a chair and a table for Rs. 6000. He sells the chair at a loss of 10% and the table at a gain of 10%. He still gains Rs. 100 on the whole. The cost price of the chair is
(1) Rs. 2500
(2) Rs. 2850
(3) Rs. 3050
(4) Rs. 3500

Answers And Solutions :
1.(2)
Let the lowest score of the cricketer be x. 
∴ Cricketer’s highest score
= x + 100
 ∴x + x + 100 = 30 × 42-40×28
=> 2x + 100 = 1260 - 1120 = 140
=> 2x = 40
=> x = 20
∴ His highest score in an innings
= 120

2.(2) Boys : Girls = 6 : 5
∴ Girls => 6/11×66=36
Boys = 30
New ratio = 30 : (36+4)
= 30 : 40 = 3 : 4

3.(1)Let the number of passes be 3x and that of failures be 2x in the exam.
∴ (3x+12)/2x=21/10
=> 42x -30x = 120
=> 12x = 120
∴x=120/12=10
so Number of students who have passed the exam=30

4.(2) Difference = Principal (r/100 )^2
=> 72 = 5000 (r/100 )^2
= r^2 = (72×10000)/5000=144
∴r= √144 = 12% per annum

5.(3) Let B’s present share = Rs. x.
∴(3903-x)(1+4/100 )^7
= x (1+4/100 )^9
=>(3903-x)=x(26/25 )^2=676x/625
=> 3903×625- 625x = 676x
=> 1301x = 3903×625
=> x = (3903×625)/1301
= Rs. 1875

6.(1)
7.(2) Single equivalent discount
= (20+5-(20×5)/100)%=24%
∴ C.P. of the trade
= Rs. ((25000×76/100)
= Rs. 19000
∴ Actual C.P.
= Rs. (19000+1000)
= Rs. 20000
∴ Profit percent
= 5000/20000×100=25%
8.(1)
9.(3)
10.(1)If the  CP of the chair be Rs. x
then,
Total S.P.
= x × 90/100+((6000-x)×110)/100
=> 9x/10+((6000-x)11)/10=6100
=> 9x+ 66000-11x=61000
=> 2x = 66000-61000=5000
=> x=Rs.2500


Find solutions for all the questions at the end of each set:

Set B


1.Average age of a couple is 25 years at the time of marriage. After  3 years, they have a two year old baby. The average age of the family is
(1) 29 years 
(2) (19) 1/3 years
(3) (17) 2/3 years 
(4) 20 years

2.A shopkeeper allows a discount of 10% on the marked price. How much above cost price must he mark his  goods (in per cent) to gain 8%?
(1) 10  
(2) 20
(3) 15  
(4) 18
 
3.A gardener has 1000 plants. He wants to plant them in such a way that the number of rows and columns remains same. Then what will be the minimum number of more plants he will need for this?
(1) 35  
(2) 25
(3) 24  
(4) 34
 
4.In an alloy of brass, the ratio of copper to zinc is 7 : 4. If 6 kg of zinc be added in 33 kg of such a quality of brass. Then the new ratio of copper to zinc is
(1) 5 : 4  
(2) 6 : 5
(3) 7 : 6  
(4) 8 : 7
 
5.Tapas deposited a certain sum of money in a post office at 12% p.a. for 4 years and deposited an equal amount in a bank for 5 years at 15% p.a. If the difference in the interest from the two sources is Rs. 1,890, the sum deposited in each case is
(1) Rs. 5,000 
(2) Rs. 9,000
(3) Rs. 7,000 
(4) Rs. 8,000
 
6.A man rides at the rate of 350 metres per minute and stops for 6 minutes to change horses at the end of every sixth kilometer. Then to travel a distance of 84 km, the time taken by the man is
(1) 3 hours 15 minutes
(2) 6 hours 17 minutes
(3) 5 hours 18 minutes
(4) 2 hours 17 minutes
 
7.Of the two persons, first person can complete a work in 32 days and second person can complete the work in 40 days. Both the persons worked together for 10 days and then the second person leaves. The number of days taken by the first person to finish the balance work is 
(1) 16  
(2) 14
(3) 21  
(4) 7
 
8.The  cost of painting the surface area of a hollow cylinder of length 70 cm and having a diameter 42 cm (negligible thickness) at the rate of 20 paise per sq. cm is
(1) Rs. 3,796 
(2) Rs. 3,896
(3) Rs. 3,996 
(4) Rs. 3,696
 
9.Average age of a class is 14.4 years. Average age of boys is 15 years and average age of girls  is 14 years. Ratio of number of girls to number of boys is
(1) 2 : 3  
(2) 3 : 2
(3) 1 : 3  
(4) 1 : 4
 
10.In an examination, 63% passed in Mathematics, 53% passed in English and 24% failed in both the subjects. If 80  candidates passed in both the subjects, 74 candidates
(1) passed only in Mathematics
(2) failed in both the subjects 
(3) passed only in English
(4) failed in Mathematics


Answer Key
1.(2) At the time of marriage,
Husband + Wife = 2×25
= 50 years
Sum of the present ages of husband, wife and child
= 50 + 6 + 2 = 58 years
∴ Required average age = 58/3 => 19 1/3 years
 
2.(2) C.P. = Rs. 100, Marked price = Rs. x
∴ (x×90)/100 = (100×108)/100
=> 9x/10 = 108
=> x = (108×10)/9=120
i. e. 20% above the cost price.

3.(3) 31 <√1000<32
32×32=1024
∴ Number of extra plants required =l024-1000=24
 
4.(3) In 33 kg of alloy,
Copper = 7/11 × 33 = 21 kg
Zinc  = 4/11 × 33 = 12 kg
On adding 6 kg of zinc,
Required ratio = 21 : (12 + 6)=> 21 : 18 = 7 : 6
 
5.(3) S.I.
=  (principal×Rate×Time)/100
Amount deposited = Rs. x
Interest from post office
= (x×12×4)/100 = Rs. 12x/25 
Interest from bank
= (x×15×5)/100=Rs.3x/4
∴ 3x/4-12x/25 = 1890
=> (75x-48x)/100 = 1890
=> 27x/100 = 1890
=> x=(1890×100)/27 = Rs. 7000

6.(3) Speed of horse rider
= 350 metre/minute
= 350/1000 × 60kmph = 21kmph
84÷6=14
i.e. he will change the horse 13 times.
Time taken in changing horses
= 13×6=78 minutes
Time taken in convering 84 km
= 4 hours
Total time = 4 hours + 78 minutes
= 5 hours 18 minutes

7.(2) Work done by first man in
1 day = 1/32
work done by second man in
1 day = 1/40
Work done by both men in 10 days
= 10 (1/32+1/40)
= 10((5+4)/160)=9/16
Remaining work = 1-9/16 = 7/16,
Which will be completed by, first man.
∴ Required time = 7/16 = 32
=14 days
 
8.(4)
9.(2) Boys = x and girls = y
∴ 14.4 = (15 × x+14 × y)/(x+y)
=>14.4x + 14.4y = 15x + 14y
=>15x-14.4x = 14.4y-14y
=>0.6x = 0.4y
=>y/x=0.6/0.4=3∶2
 
10.(4)


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