1.
To harvest 216 cubic metre of wheat 2 days before the planned date, how many cubic metres of wheat must be harvested by team over and the above the plan every day after first three days?
Answer: Option 'B'
Amount of wheat harvested in first three days = 24 × 3 = 72 m3
Remained = 216 - 72 = 144 m3
This has to be harvested in n - 3 - 2 = 4 days
Required Harvest per day = 144/4 = 36 m3
Required additional harvest per day = 36 - 24 = 12 m3
2.
What is the probability of drawing at least one red ball?
Answer: Option 'B'
The probability of at least one red ball = 1 - (probability of no red ball)
= 1 - (1/2) × (1/2) × (1/2) × (1/2)
= 1 - (1/16)
= 15/16
3.
A and B started a business with the investments in the ratio of 5 : 3 respectively. After 6 months from the start of the business, C joined them and the respective ratio between the investments of B and C was 2 : 3. If the annual profit earned by them was Rs. 12300, what was the difference between B’s share and C’s share in the profit?
Answer: Option 'A'
A : B = 5 : 3 = 10 : 6
B : C = 2 : 3 = 6 : 9
A : B : C = 10 : 6 : 9
Ratio for 1 month = (10x × 12) : (6x × 12) : (9x × 6) = 20 : 12 : 9
= 20 : 12 : 9
Required difference = (12 - 9)/41 = 12300 = 900 Rs.
4.
A cricketer gives 12.4 runs per wicket. He gives 26 runs and take 5 wickets in a match after which his average becomes 12 runs per wicket. How many wickets had been taken by him excluding the last match?
Answer: Option 'D'
Let number of wickets before last match = x
Total runs given till last match = 12.4 × x
(12.4 × x)/(x+5) = 12
x = 85
5.
What are the approximately average speeds of Bus A and Bus B?
Answer: Option 'A'
Average speed of bus A = 600/[(20/40)+(200/50)+(200/60)] = 48.64 km/hr
Average speed of bus B = 600/[(200/60)+(200/40)+(200/50)] = 48.64 km/hr
6.
A watch dealer sells watches at Rs. 600 per watch. However, he is forced to give two successive discounts of 10% and 5% respectively. However, he recovers the sales tax on the net sale price from the customer at 5% of the net price. What price does a customer have to pay him to buy a watch?
Answer: Option 'B'
600 - 10% of 600 = 540 & 540 - 5% of 540 = 513
513 + 5% of 513 = 538.65
7.
How many cubic metres of wheat a day did the team have to cut according to the plan?
Answer: Option 'C'
Let, the planned no. of days be 'n' and planned harvest per day be 'x' m3
Then, nx = 216
ATQ, x(n-1) + 8(n-4) = 232
or, nx - x + 8n - 32 = 232
or, 8n - x = 48
or, 8n - 216/n = 48
or, 8n2 - 48n - 216 = 0
or, n2 - 6n - 27 = 0
=> (n-9)(n+3) = 0
=> n = 9
Hence, x = 216/9 = 24 m3
8.
If each bag a green ball is added, then find the probability of drawing at least one blue ball?
Answer: Option 'A'
The probability of at least one blue ball = 1 - (probability of no blue ball)
= 1 - (2/3) × (2/3) × (2/3) × (2/3)
= 1 - (16/81)
= 65/81
9.
Ganesha was hired on the basis of commission in NICL and got the bonus only on the first years commission. He got the policies of Rs. 2 lakh having maturity period of 10 year. His commission in the first, second, third, fourth and for the rest of the years is 20%, 16%, 12%, 10% and 4% respectively while bonus is 25% of the commission. If the annual premium is Rs. 20,000 then what is his total commission if the completion of the maturity of all the policies is mandatory?
Answer: Option 'B'
10.
When and where will the two buses cross each other?
Answer: Option 'C'
Bus A travels first 1/3 rd of the distance in 200/40 = 5 hrs
Bus B travels first 1/3 rd of the distance in = 200/60 = 10/3 hrs
in 5 - 10/3 = 5/3 hrs Bus B travels another 5/3 × 40 = 200/3 kms
Now, the distance between Buses A and B reduces 600 - (200 + 800/1) = 400/3 kms
This is covered by both in (400/1)/(60+40) = 1(1/3) hr
Hence, they will cross each other after = 5 + 1(1/3) = 6 hrs 20 minutes
And the point of crossing is 200 + 80 = 280 kms from city M