1. Rs 1087 was divided among A, B, and C. Such that if Rs. 10, 13 and 14 be diminished form their shares respectively, the remainders will be in the ratio of 3 : 5 : 7. What is the share of A?
(1) Rs. 220
(2) Rs. 210
(3) Rs. 310
(4) Rs. 320
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Explanation :
(1) Sum of money to be divided
= Rs. 1087
Total money to be withdrawn
= Rs (10 + 13 + 14) = Rs. 37
Remainder = Rs. (1087 – 37)
= Rs. 1050
If is to be divided in the ratio
3 : 5 : 7
Therefore Share of A
= Rs. (210 + 10) = Rs. 220
2. A can do a piece of work in 6 days. B takes 8 days and C takes as long as A and B and C working together will complete the work in :
(1) 2 2 / 5 days
(2) 2 2 / 11 days
(3) 3 3 / 7 days
(4) 3 2 / 5 days
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Explanation :
(1) (A + B)S 1 day’s work
= 1 / 6 + 1 / 8 = 7 / 24
Therefore (B + C)’s 1 day’s work
= 1 / 8 + 7 / 24 = 5 / 12
Therefore B and C together will complete the work in
12 / 5 = 2 2 / 5 days
3. A cistern is normally filled in 8 hours but takes 2 hours longer to be filled because of a leak in the bottom. If the cistern id full the leak will empty in :
(1) 20 hrs
(2) 36 hrs
(3) 40 hrs
(4) None f these
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Explanation :
(3) Let leak cn empty the full tank in x hours.
1 / 8 – 1 / x = 1 / 10
Therefore 1 / x = 1 / 8 – 1 / 10 = 1 / 40
Therefore x = 40
4. A person sets to cover a distance of 12 km in 45 minutes, If the covers 3 / 4 of the distance in 2 / 3 rd time. What should be his speed to cover the remaining distance in the remaining time?
(1) 16 km/hr
(2) 18 km/hr
(3) 12 km/hr
(4) 14 km/hr
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Explanation :
(3) Distance already covered
= 3 / 4 * 12 = 9 km
Time spent = 2 / 3 * 45 min.
= 30 min.
Distance left = (12 – 9) km
= 3 km
Time left = (45 – 30) min
= 15 min.
Therefore Reqd. speed
= 3 / 15 / 60 km/hr. = 12 km/hr.
5. The diameter of a circle is 105 cm, less than the circumference. What is the diameter of the circle?
(1) 42 cm
(2) 44 cm
(3) 48 cm
(4) 49 cm
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Explanation :
(4) Let radius = r
2 pie r – 2r = 105
Therefore 2 r = 105 / pie – 1 = 105 / 22 / 7 – 1 = 49
6. A and B enter into a partnership by making investments in the ratio 1 : 2, 5% of the total profit goes to chairty. If B’s share is Rs 760 total profit is :
(1) Rs. 1200
(2) Rs. 1800
(3) Rs. 2400
(4) Rs. 1560
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Explanation :
(1) Let Rs x be the total profit.
Profit available for distribution among A and B = 9.5x This is to be distributed in the ratio = 1 : 2
Therefore 2 / 3 * 0.95 * = 760
= x = 1200
7. The simple interest on a sum of money is 1 / 9 of the principal and the number of years is equal to the rate percent per annum. The rate percent per annum is :
(1) 100 / 9 %
(2) 10 / 3 %
(3) 5 / 3 %
(4) None of the these
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Explanation :
(2) Let Principal = Rs x and rate
= r % Then interest
= 1 / 9 x and no. of years
= r Therefore x / 9 = x * r * r / 100
Therefore r^2 = 100 / 9 = r = 10 / 3
8. A motorboat can row 25 km up stream and 39 km downstream in 8 hours. Also it can go 35 km upstream and 52 km downstream in 11 hours. The rate (in km/hr) of flow is :
(1) 5
(2) 4
(3) 8
(4) 6
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Explanation :
(2) Let rate upstream
= x km/hr.
and rate down stream
= y km/hr.
Then 25 / x + 39 / y = 8… (I)
and 35 / x + 52 / y = 11… (II)
Multiplying (I) by 7 and (II) by 5
and subtracting 13 / y = 56 – 55
Therefore y = 13
Therefore (I) = 25 / X = 8 – 3 = 5
Therefore x = 5
Therefore Rate of flow = 1 / 2
(13 – 5) = 4km/hr.
9. At an election where there are two candidates only. the candidate who gets 43% of the votes is rejected by a margin of 420 votes. The total number of votes polled were :
(1) 3000
(2) 3500
(3) 2500
(4) 2800
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Explanation :
(1) Let no. of votes polled = xNO.
of votes of lossing candidate
= 0.43 x
No. of votes of winning candidate
= x – 0.43 x
= 0.57 x
Therefore 0.57 x – 0.43 x = 420
0.14 x = 420
x = 3000
10. A can do a work in 6 days and B in 9 days. How many days will both take together to complete the work?
(1) 7.5
(2) 5.4
(3) 3.6
(4) 3
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Explanation :
(3) According to question,
A can finsih the whole work in 6 days.
Therefore A’s one day’s work = 1 / 6
Similarly,
B’s one day’s work = 1 / 9
(A + B)’s one day’s work
= (1 / 6 + 1 / 9) = (3 + 2 / 18) = 5 / 18
Therefore, (A + B)’s can finish the
whole work in 18 / 5 days i.e. 3.6 days