Mock Test 2 Arithmetic Answers with Explanations
- A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of:
Explanation:
C.P. = Rs. 3000.
S.P. = Rs. | 3600 x 100 | = Rs. 3000. | ||
100 + (10 x 2) |
Gain = 0%.
2. A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Explanation:
C’s 1 day’s work = | 1 | – | 1 | + | 1 | = | 1 | – | 7 | = | 1 | . | ||
3 | 6 | 8 | 3 | 24 | 24 |
A’s wages : B’s wages : C’s wages = | 1 | : | 1 | : | 1 | = 4 : 3 : 1. |
6 | 8 | 24 |
C’s share (for 3 days) = Rs. | 3 x | 1 | x 3200 | = Rs. 400. | ||
24 |
3. A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
Explanation:
Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs. [ (6500 x 6) – 34009 ]
= Rs. (39000 – 34009)
= Rs. 4991.
4. Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
Explanation:
L.C.M. of 2, 4, 6, 8, 10, 12 is 120.
So, the bells will toll together after every 120 seconds(2 minutes).
In 30 minutes, they will toll together | 30 | + 1 = 16 times. |
2 |
5.Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
Explanation:
Since first and second varieties are mixed in equal proportions.
So, their average price = Rs. | 126 + 135 | = Rs. 130.50 | ||
2 |
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
By the rule of alligation, we have:
Cost of 1 kg of 1st kind Cost of 1 kg tea of 2nd kind | ||
Rs. 130.50 | Mean Price Rs. 153 |
Rs. x |
(x – 153) | 22.50 |
x – 153 | = 1 | |
22.50 |
x – 153 = 22.50
x = 175.50
6. A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:
Explanation:
Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
A’s share = Rs. | 35000 x | 21 | = Rs. 14,700. | ||
50 |
7. The reflex angle between the hands of a clock at 10.25 is:
Explanation:
Angle traced by hour hand in | 125 | hrs = | 360 | x | 125 | º | = 312 | 1 | º | . | ||
12 | 12 | 12 | 2 |
Angle traced by minute hand in 25 min = | 360 | x 25 | º | = 150º. | ||
60 |
Reflex angle = 360º – | 312 | 1 | – 150 | º | = 360º – 162 | 1 | º | = 197 | 1 | . | ||
2 | 2 | 2 |