IBPS Clerk Prelims: Quants Day 9

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Stratus – IBPS Clerk Course 2015 

Stratus - IBPS Clerk - Daily Test - Quants
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  1. The ratio of ages of A and B 5 years ago was 3 : 5. 10 years hence this ratio will be 7 : 10. Find the ratio of their present ages.
    A) 15 : 24
    B) 16 : 25
    C) 11 : 17
    D) 11 : 23
    E) None of these
    Answer & Explanation
    B) 16 : 25
    Explanation:

    Let ages 5 years ago be A and B.
    So A/B = 3/5
    Then A+15/B+15 = 7/10
    Solve both equations
  2. A and B started a business. A invests Rs 5200. B invests Rs 3000. After 6 months B invests Rs 3000 more and C also joins and invests Rs 7000. Find the ratio in which the profits will be shared among them.
    A. 55 : 42 : 35
    B. 52 : 42 : 35
    C. 52 : 45 : 35
    D. 52 : 45 : 38
    E. None of these
    Answer & Explanation
    C. 52 : 45 : 35
    Explanation:

    So A’s share : B’s share : C’s share
    5200 * 12 : 3000 * 6 + 6000 * 6 : 7000 * 6
    52 : 45 : 35
  3. A does a work in 6 days and B does the same work in 14 days. They started the work alternately starting with A. After how many days the work will be completed?
    A) 7 days
    B) 8 2/7 days
    C) 8 days
    D) 9 2/5 days
    E) None of these
    Answer & Explanation
    B) 8 2/7 days
    Explanation:

    LCM (6, 14) = 42
    So total work = 42
    A’s efficiency = 42/6 = 7
    B’s efficiency = 42/14 = 3
    2 days work (A+B) = 7+3 = 10
    Multiply by 4 both side
    8 days work (A+B) = 40
    Remaining work = 42 – 40 = 2
    Now A’s turn, he will complete remaining work in 2/7 day
    So total 8 2/7 days.
  4. There are 2 white, 3 black and 5 green balls. 3 balls are drawn at random. What is the probability of drawing the balls with at least 2 black balls?
    A) 13/40
    B) 21/60
    C) 11/60
    D) 11/54
    E) None of these
    Answer & Explanation
    C) 11/60
    Explanation:

    Total ways = 10C3 = 10*9*8/3*2*1 = 120
    There are 2 cases:
    Case 1 : 2 black balls
    Ways are 3C2 * 7C1 = 21
    Case 2 : 3 black balls
    Ways are 3C3 = 1
    So prob. = 21+1 / 120 = 22/120 = 11/60
  5. The area of the inner part of the cylinder whose radius is half that of its height is 3080 sq. cms. How many litres of milk can the cylinder contain?
    A) 17.248 litres
    B) 19.68 litres
    C) 17.42 litres
    D) 15.248 litres
    E) None of these
    Answer & Explanation
    A) 17.248 litres
    Explanation:

    r = ½ h
    inner area = 2ᴨrh +ᴨr2
    so, 2ᴨ * 1/2 h * h + ᴨ 1/4 h2 = 3080
    5/4 * 22/7 * h2 = 3080
    Solve, h = 28, so r = 1/2 * 28 = 14
    Volume = ᴨ r2h = 22/7 * 142 * 28
  6. A bucket contains 600 coins of 25 paise denomination and 1200 coins of 50 paise denomination. Now 12% of 25 p coins and 24% of 50 p coins are removed from the bucket. What is the percentage of money removed from the bucket (nearly)?
    A) 15.6%
    B) 30%
    C) 21.6%
    D) Cannot be determined
    E) None of these
    Answer & Explanation
    C) 21.6%
    Explanation:

    Total money = 25/100 * 600 + 50/100 *1200 = 750
    25 p removed = 12/100 * 600 = 72
    50 p removed = 24/100 * 1200 = 288
    Total money removed = 25/100 * 72 + 50/100 * 288 = 162
    So % = 162/750 * 100
  7. How many kilograms of rice costing Rs 8 per kg must be mixed with 36 kg of rice costing Rs 5.40 per kg so that there is a gain of 20% by selling the obtained mixture at Rs 7.20 per kg?
    A) 10.2 kg
    B) 10.8 kg
    C) 12.8 kg
    D) 11.2 kg
    E) None of these
    Answer & Explanation
    B) 10.8 kg
    Explanation:

    SP = 7.20, Profit% = 20%. So CP = 100/120 * 7.20 = Rs 6
    By allegation method:
    800 paise                         540 paise
    .                   600 paise
    60                                       200
    So ratio = 60 : 200 = 3 : 10
    This gives 3/10 = x/36
    Solve, x = 10.8
  8. At compound interest per annum, a certain sum amounts to Rs 6690 after 3 years and to Rs 10035 after 6 years. Find the principal sum invested.
    A) Rs 5260
    B) Rs 4840
    C) Rs 4460
    D) Rs 4640
    E) None of these
    Answer & Explanation
    C) Rs 4460
    Explanation:

    P [1 + r/100]6 = 10035
    P [1 + r/100]3 = 6690
    Divide both equations. This gives
    [1 + r/100]3 = 10035/6690 = 3/2
    Put this in second equation:
    P * 3/2= 6690
    P = 4460
  9. To gain 33% on an article even after giving a discount of 5%, at what percentage above the cost price should the article be marked?
    A) 40%
    B) 50%
    C) 42%
    D) 62%
    E) 55%
    Answer & Explanation
    A) 40%
    Explanation:

    Let CP = 100
    Use MP = (100+p%)/(100-d%) * CP
    MP = 133/95 * 100 = 140
    So required % = 140 – 100 / 100 * 100 = 40%
  10. A train reaches its destination on time when it moves at an average speed of 50 km/hr, and when the average speed is 45 km/hr, then it reaches 20 minutes late at same place. Find the length of journey.
    A) 162 km
    B) 150 km
    C) 170 km
    D) 128 km
    E) None of these
    Answer & Explanation
    B) 150 km
    Explanation:

    Difference in time = 20/60 min
    Distance = 50*45/50-45 * 20/60 = 150