1. In how many ways 10 mangoes can be divided among 4 children?
1) 280
2) 286
3) 284
4) 278
5) 282
Directions: 7 boys and 7 girls sit in a row randomly. Find the probability that –
2. The girls sit together.
1) 1/429
2) 2/429
3)3/421
4) 1/421
5) 1/427
3. The boys and girls sit alternatively.
1) 1/1715
2) 2/1715
3) 8/1715
4) 5/1714
5) 1/1716
4. What will be the length of the diagonal of a square park whose area is equal to the area of a rectangular park of length 160 m and breadth 80 m?
1) 180 m
2) 185 m
3) 172 m
4) 175 m
5) 160 m
5. A train left from station A for station B at 4 pm at an average speed of 80 km/h. At 8 pm, another train also had left from station A for station B on a parallel track at an average speed of 120 km/h. How far from A, is the another train expected to overtake the first train?
1) 900 km
2) 940 km
3) 960 km
4) 980 km
5) 920 km
6. 8 men can complete a piece of work in 12 days. 10 women can do the same piece of work in 15 days where as 18 children can complete in 10 days. 8 men, 25 women and 30 children work together for 2 days. If only men were to complete the remaining work in 1 day, how many men would be required totally?
1) 25
2) 16
3) 18
4) 30
5) 20
7. A man buys a T.V valued at Rs. 36000. He pays Rs. 12000 at once and rest 18 months later on which he is charged simple interest at the rate of 6% p.a. Find the total amount he pays for t.v.
1) Rs. 38180
2) Rs. 38460
3) Rs. 38860
4) Rs. 38160
5) Rs. 38260
8. A shopkeeper sells note book at the rate of Rs. 65 each and earns a commission of 5%. He also sells pen stand at Rs. 90 each and earns a commission of 15%. How much commission will he earn in two weeks, if he sells 12 note books and 8 pen stands a day?
1) Rs. 2058
2) Rs. 2158
3) Rs. 2258
4) Rs. 2048
5) Rs. 2068
9. Two partners invest Rs. 1,20,000 and Rs. 80,000 respectively in a business and agree that 30% of the profit should be divided between them and the remaining profit is to be treated as interest on capital. If one partner gets Rs. 1860 more than the other, find the total profit made in the business.
1) Rs. 31000
2) Rs. 30000
3) Rs. 28000
4) Rs. 32000
5) Rs. 29000
10. A trader has 130 kg of pulses, part of which he sells at 12% profit and the rest at 25% profit. He gains 18% on whole. What is the quantity sold at 25% profit?
1) 65 kg
2) 60 kg
3) 70 kg
4) 64 kg
5) 68 kg
Answers:
1. 2; Required number of ways
= n + r – 1 Cr – 1
= 10 + 4 –1 C4–1
= 13C3
= 13! / 3! 10!
= (13 * 12 * 11)/ (3*2)
= 286
2. 1;
When 7 girls sit together, regarding them as one group
(7 boys + 1 group of girls) = 8 objects.
Required probability = 8! * 7!/14!
= 1/429
3. 5;
If we begin with boy, then 7 boys can sit in 7 odd places in 7! ways and 7 girls in 7 even places in 7! ways, Therefore total ways = 7! × 7!. Similarly, if we begin with girls then 7! × 7!
Required probability = 2 * 7! * 7!/ 14!
= 1/1716
4. 5
1/2 * Diagonal^2 = 160*80
D = sqroot(2*160*80) = 160m
5. 3
Distance travelled by first train in 4 h = 80 × 4 = 320 km
Relative speed = (120 – 80) = 40 km/hr
Let x be the time taken by the second train to overtake
the first train.
Then, 40 = 320/x
x = 8h
Distance from A = 120 * 8 = 960km
6. 2; (8 × 12) men = (10 × 15) women = (18 × 10) children
16 men = 25 women = 30 children
Now, 8M + 25W + 30C = 8M + 16M + 16M = 40 men
8 men’s 1 day work = 1/12
40 men's 1 day work = 1/12 * 40/8 = 5/12
40 men's 2 day work = 5/12 * 2 = 5/6
Remaining Work = 1 - 5/6 = 1/6
Remaining work will be completed by 40 men in 2/5 days.
To complete in one day man required = 40 * 2/5 = 16 men
7. 4
Interest charge on (36000 – 12000 = 24000)
= (24000 * 18 * 6)/(100 * 12) = 2160
The total amount paid for T.V
= 12000 + 24000 + 2160 = Rs. 38,160
8. 1;
12 notebooks in a day, then in two weeks (i.e. 14 days)
= 14 × 12 = 168 notebook
Commission earned = 65 × 168 × 5/100 = Rs. 1546
8 pen stands in a day, then in two weeks (i.e. 14 days)
= 8 × 14 = 112 pen stands
Commission earned = 112 × 90 × 15/100 = Rs. 1512
Total commission earned = 546 + 1512 = Rs. 2058
9. 1; The ratio of profit = 12 : 8 = 3 : 2
Total Profit = 1860 (100/30)(3+2/3-2)
= 1860 * 100/30 * 5 = Rs. 31000
10. 2
The quantity sold at 25% profit
Where, N = total quantity, P = % gain on whole
x = part sold at x% profit
y = part sold at y% profit
= (p-x/y-x)N
= (18-12)/(25-12) * 130
6/13 * 130 = 60kg