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Directions (1-5): Study the given passage carefully and answer the questions.   Rahul, Sandy and Sati invested in ratio 2 : 3 : 4. After 4 months Sandy added Rs. 1500 more in his investment and Rahul withdrew Rs. 800 from his investment. After six months more Sati invested half of the investment done by Rahul in first four months and Sandy invested 50% more than the investment done by Sati in first 10 months. Rahul invested same as investment done by Sandy in first four months. Ratio of profit of Sati to total profit at the end of year is given as 125 : 376.

1. Profit of Sandy is approximately what percent of total profit?

(a) 64% (b) 48% (c) 72%  (d) 68% (e) 42%

2. What is the difference between profit share of Rahul and Sandy if total profit is Rs.37,600?
(a) 12,000 (b) 16,400 (c) 18,500  (d) 22,900 (e) 20,000

3. Veer have 250% more than initial investment of Sati for a year. Find total interest earned by him if he invested his amount in a scheme which offers 20% p.a. for 2 years?

(a) Rs. 1400 (b) Rs. 1500 (c) Rs. 1540   (d) Rs.1600 (e) Rs.1640

4. What is the average of profit share of Sandy and Sati out of total profit of Rs. 37,600?    (a) 18,220 (b) 18,250 (c) 16,420 (d) None of these (e) 12,490

5. If initial investment of Bhavya is one-third of initial investment of Rahul, Sandy and Sati together then find the difference between initial investment of Bhavya and Rahul.

(a) Rs.1000  (b) None of these (c) Rs.750  (d) Rs.500 (e) Rs.250

6. 150 kg of alloy containing copper and zinc in the ratio 3 : 2 mixed with ‘X’ kg of alloy containing copper and zinc in the ratio 2 : 3. If the overall alloy should contain copper between 45% to 55%, what can be minimum value of X?

(a) 450 kg (b) 100 kg (c) 50 kg  (d) Cannot be determined (e) None of these

7. Three different liquids which have 10% water, 20% water and x% of water are mixed in the ratio of their quantity 2 : 3 : 4 respectively. If 12% of water is present in final mixture. Calculate value of x.

(a) 9% (b) 20% (c) 7%  (d) 15% (e) 17%

8. ‘x’ liters of a 30% alcohol solution is mixed with 40 liters of 60% alcohol solution & a resultant of 50% alcohol solution is formed. Now ‘3x’ liters of y% alcohol solution is added to 30 liters of 50% alcohol solution which resulted in 45% alcohol solution. The ratio of y : x is

(a) 17 : 6  (b) 16 : 15 (c) 7 : 15  (d) 14 : 5 (e) 17 : 8

9. There are three varities of sugar with their quantity in the ratio of 3 : 4 : 5. If 9 kg of first variety and 4 kg of second variety are added to their respective quantity and x kg of 3rd type is removed from it, then final ratio becomes 9 : 10 : 10. Find the sum of initial quantities of these varieties.

(a) 120 kg (b) 96 kg  (c) 84 kg (d) 108 kg (e) None of these

10. A jeweler mixed gold and copper in 2 proportion. In type ‘A’ alloy, 6 gm gold is mixed with 5 gm copper and in type ‘B’ alloy, 5 gm gold in mixed with 3 gm copper. If jeweler have 122 gm gold and 90 gm copper, then find the weight of type ‘B’ alloy.

(a) 60 gm  (b) 80 gm (c) 70 gm   (d) 100 gm (e) 90 gm

Solutions-
Solutions (1-5)
Let investment of Rahul, Sandy and Sati be 2x, 3x and 4x respectively.  Ratio of profit Rahul : Sandy : Sati 2x × 4 : 3x × 4 : 4x × 10 +(2x – 800)×6  +(3x+1500)× 6 +(5x × 2) +(5x–800)× 2 (9x +1500) × 2 30x – 6400 : 48x + 12000 : 50x  ATQ, 50x128x+5600 = 125376 ⇒ x = 250 Ratio of profit share of Rahul, Sandy and Sati is 1100∶24000∶12500→11∶240∶125

1. (a); Required percentage = 240376×100   = 63.829% ≃ 64%

2. (d); Required difference    = 240−11376×37600=22,900

3.  (c); Investment of Veer    = 4×250×350100=3500 Interest earned by Veer    = 3500[1+20100]2−3500=1540

4.  (b); Required average = 240+1252×37600376 =18,250

5.  (e); Investment of Bhavya = 2x+3x+4x3 = 3x   = 3 × 250 = Rs.750 Required profit = 750 - 2×250  = 750 – 500 = 250

6. (c); If overall alloy contain copper as 45%    (150×35+2x5)=45100(150+x) (90+2x5)=920(150+x)   1800+8x=1350+9x x = 450 kg If overall alloy contain copper as 55%    (90+2x5)=55100(150+x) 1800 + 8x = 1650 + 11x 3x = 150 ⇒ x = 50 kg   Minimum value of X is 50 kg

7. (c); Let the quantity of three liquids is 200a, 300a and 400a   10% of water in first type means 20a water 20% of water in second type means 60a water   x% of water in third type means 4xa water ∴ ATQ, (20a+60a+4xa)/900a = 12/100 ⇒ 4xa = 108a – 80a     ⇒ x = 28a/4a = 7

8. (e); From statement I    x×30100+40×60100(x+40)=12   ⇒ (2400+30x)100(x+40)=12 ⇒ x=20    Now from statement II (3x×y100+30×50100)3x+30=45100    Here 3X = 3 × 20 = 60 litres ⇒ (60y100)+1590 = 45100 ⇒    60y100 = 812–15 ⇒ y = 42.5 ∴ y∶x = 42.5 : 20 = 17 : 8

9. (d); Let the initial quantity is 3y, 4y & 5y of these varities   According to condition 3y+9∶ 4y+4∶ 5y –x=9∶10∶10 From 1st 2 ratios    ⇒ 3y+94y+4=910 ⇒ y=9, Hence sum of initial quantities is (3 + 4 + 5) × 9   = 108 kg NOTE: No need calculate Value of x

10. (b); Let gold and copper in Type A alloy be 6a and 5a    Let gold and copper in type B alloy 5b and 3b ⇒ 6a+5b=122 … (i)    5a+3b=90 … (ii) Solving equation (i) and (ii) we get a=12 ⇒  b=10 Weight of type ‘B’ alloy = (5 + 3) × 10 = 80 gm