1. A shopkeeper bought 25 kg of Rice at rate of Rs.40 per kg. He sold 60% of the total quantity at the rate of Rs.50 per kg. Exactly, at what price per kg should he sell the remaining quantity to make 50% overall profit ?
A. 85
B. 80
C. 75
D. 70
E. None of these
Sol. CP of Rice = 25 * 40 = 1000
60% of 25 kg = 15 kg
SP of 15kg = 15 * 50 = 750
150/100 * 1000 = 1500
Difference = 1500 – 750 = 750
SP of 10kg = 750
SP of 1kg = 75
2. The smallest side of a right-angled triangle is 8 cm less than the side of a square of perimeter 56 cm, The second largest side of the right-angled triangle is 4 cm less than the length of the rectangle of area 96 sq cm and breadth 8 cm. What is the largest side of the right-angled triangle ?
A. 20 cm
B. 15 cm
C. 10 cm
D. 25 cm
E. None of these
Sol. Smallest side of a right-angled triangle = 1/4 (Perimeter of Square) – 8
= 1/4 (56) – 8 = 14 – 8 = 6
second largest side of the right-angled triangle = 96/8 – 4 = 8
largest side of the right-angled triangle = sq.root of (6 * 6 + 8* 8) = 10 cm
3. X, Y and Z started a business with their investments in the ratio 1:3:8. After 6 months, X invested the half amount more as before and Y invested twice the more as before, while Z withdraws 1/4 th of their investments. Find the ratio of their profits at the end of the year is ?
A. 5:24:28
B. 3:5:10
C. 1:2:3
D. 3:7:12
E. None of these
Sol. Investment of X for 1 year = x*6 + (x + x/2)6 = 15x
Investment of Y for 1 year = 3x*6 + (3x + 6x)6 = 72x
Investment of Z for 1 year = 8x*6 + (8x – 8x/4)6 = 84x
Ratio = 15x : 72x : 84x = 5:24:28
4. A butler stole wine from a butt of sherry which contained 80% of spirit and he replaced it by wine containing only 32% of spirit. The butt was now only 48% strong. How much of the butt did he steal ?
A. 1/3
B. 2/3
C. 1/5
D. 2/5
E. None of these
Sol. 32 ———- 80
48
32 ———- 16
Ratio = 2:1
butler stole 2/3 of butt.
5. The ratio of the adjacent angles of a parallelogram is 7 : 8. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?
A. 168
B. 188
C. 224
D. 216
E. None of these
Sol. Sum of the adjacent angles of Parallelogram = 180°
Smaller angle of Parallelogram = 7/15 * 180 = 84°
Second largest angle of the quadrilateral = 7/30 * 360 = 84°
Sum = 84° + 84° = 168°
6. Shopkeeper purchased some goods for Rs.900 and sold one-third of the goods at a loss of what 12%, then at gain % should the remainder goods he sold to gain 18% profit on the whole transaction ?
A.31%
B.26%
C.33%
D.18%
E.None of these
Sol. 1/3rd at 12% loss = 900/3 = (300*88)/100 = 264
(900*18)/100 = 108
600 + 162 + 36 = 798
(198/600)*100 = 33%
7. A dealer marked the price of an item 20% above cost price. He allowed two successive discounts of 10% and 25% to a customer. A a result he incurred a loss of Rs.684. At what price did he sell the item to the customer ?
A.1670
B.2768
C.1817
D.2916
E.None of these
Sol. CP = 100
MP = 120
120*90/100 = 108; 108*75/100 = 81
Loss = 100 – 81 = 19%
CP = 100/19*684 = 3600
SP = 3600*81/100 = 2916
8. A man went to shop to buy mobile for Rs.3500, the rate of sales tax being 8%. He tell the shopkeeper to reduce the price of mobile to such an extent that has to pay Rs.3500, inclusive of all taxes. Find the reduction price.
A.Rs.210
B.Rs.260
C.Rs.320
D.Rs.140
E.None of these
Sol. (3500*100)/108 = 3240
3500-3240 = 260
9. An article passing threw two hands, is sold at profit of 40 % at the original price , if the first dealer makes a profit of 15 % , then the profit made by second dealer.
A.25%
B.26%
C.18%
D.22%
E.None of these
Sol. Total Profit = [P1 + P2 +(P1*P2/100)] 40 = 15 + P2 + (15*P2)
25-p2 = 15P2/100
2500 = 15p2+100p2
P2 = 2500/115 = 21.7% = 22%
10. What is the maximum % discount that a man can offer on her MP so that he ends up selling at no profit or loss, if he had initially marked his goods up by 35% (approximately)?
A.20%
B.32%
C.27%
D.30%
E.None of these
Sol. 35-x-(35*x/100) = 0
3500/100 –(100x+35x/100) = 0
35 = 135/100
X = 35*100/135 = 25.9 = 26%
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