Dear Reader,
Below are four problems dealing with solving equations to find unknowns.
Question 1
The cost of 4 kg rice and 8 kg wheat is Rs.320. With the same amount a man can buy 2 kg rice and 12 kg wheat. What will the cost of 24 kg rice?
a) Rs.640 b) Rs.730 c) Rs.810 d) Rs.960
Answer : d) Rs.960.
Solution :
Let the price of 1 kg rice be Rs.r
Let the price of 1 kg wheat be Rs.w
Given that, the cost of 4 kg rice and 8 kg wheat is Rs.320.
i.e., 4r + 8w = 320
r + 2w = 80 ....(1)
Cost of 2 kg rice and 12 kg wheat is Rs. 320.
i.e., 2r + 12w = 320
r + 6w = 160 ....(2)
Subtracting (1) from (2), we have 4w = 80
w = 20.
i.e., price of 1 kg wheat is Rs.20
From (1), r + 40 = 80
r = 40
Price of 24 kg rice = Rs.24 x 40 = Rs. 960.
Question 2
If 17 doors, 12 chairs and 15 tables cost Rs. 37,000 then how much does 51 doors, 45 tables and 36 chairs cost?
a) Rs.111000 b) Rs.215000 c) none of these d) cannot be determined.
Answer : a) Rs.111000.
Solution :
Let the cost of 1 door be Rs. d
Let the cost of 1 table be Rs. t
Let the cost of 1 chair be Rs. c.
We have to find the value of 51d + 36 c + 45t....(1)
Given that, 17d + 12 c + 15 t = Rs.37000...(2)
Here, we have 1 eqn and 3 unknowns. So it is impossible to find d, t and c.
But, we can find the value of (1) by simplifying as follows:
51d + 36c + 45t = 3x17d + 3x12c + 3x15t = 3(17d + 12c + 15t).
From (2), we have 3(17d + 12c + 15t) = 3(37000) = 111000.
Hence the required answer is Rs.111000.
Question 3
In a Zoo, there are some lions and parrots. If the number of legs is 6 less than 4 times the number of heads, then what is the number of parrots in the Zoo?
a) 6 b) 3 c) none of these d) cannot be determined.
Answer : b) 3.
Solution :
Let the number of lions in the Zoo be L and number of parrots be P.
Each lion has 4 legs and each parrot has 2 legs.
Therefore, Total number of legs of lions and parrots = 4L + 2P
Total number of heads = L + P
Given that, (4L + 2P) + 6 = 4(L + P)
4L + 2P + 6 = 4L + 4P
2P + 6 = 4P
2P = 6
P = number of parrots = 3.
Question 4
If in a group of dogs and crows, the number of heads is 24 and the number of feet is 70 then the number of crows will be:
a) 8 b) 13 c) none of these d) cannot be determined
Answer : b) 13.
Solution :
Let the number of dogs in the group be d and number of crows be c.
Total number of legs = 4d + 2c = 70 ...(1)
Total number of heads = d + c = 24 => 4d + 4c = 96......(2)
Now, Subtracting (2) from (1), we have, 2c = 96 - 70 = 26 => c = 13.
Hence, the required number of crows in the group is 13.
Below are four problems dealing with solving equations to find unknowns.
Question 1
The cost of 4 kg rice and 8 kg wheat is Rs.320. With the same amount a man can buy 2 kg rice and 12 kg wheat. What will the cost of 24 kg rice?
a) Rs.640 b) Rs.730 c) Rs.810 d) Rs.960
Answer : d) Rs.960.
Solution :
Let the price of 1 kg rice be Rs.r
Let the price of 1 kg wheat be Rs.w
Given that, the cost of 4 kg rice and 8 kg wheat is Rs.320.
i.e., 4r + 8w = 320
r + 2w = 80 ....(1)
Cost of 2 kg rice and 12 kg wheat is Rs. 320.
i.e., 2r + 12w = 320
r + 6w = 160 ....(2)
Subtracting (1) from (2), we have 4w = 80
w = 20.
i.e., price of 1 kg wheat is Rs.20
From (1), r + 40 = 80
r = 40
Price of 24 kg rice = Rs.24 x 40 = Rs. 960.
Question 2
If 17 doors, 12 chairs and 15 tables cost Rs. 37,000 then how much does 51 doors, 45 tables and 36 chairs cost?
a) Rs.111000 b) Rs.215000 c) none of these d) cannot be determined.
Answer : a) Rs.111000.
Solution :
Let the cost of 1 door be Rs. d
Let the cost of 1 table be Rs. t
Let the cost of 1 chair be Rs. c.
We have to find the value of 51d + 36 c + 45t....(1)
Given that, 17d + 12 c + 15 t = Rs.37000...(2)
Here, we have 1 eqn and 3 unknowns. So it is impossible to find d, t and c.
But, we can find the value of (1) by simplifying as follows:
51d + 36c + 45t = 3x17d + 3x12c + 3x15t = 3(17d + 12c + 15t).
From (2), we have 3(17d + 12c + 15t) = 3(37000) = 111000.
Hence the required answer is Rs.111000.
Question 3
In a Zoo, there are some lions and parrots. If the number of legs is 6 less than 4 times the number of heads, then what is the number of parrots in the Zoo?
a) 6 b) 3 c) none of these d) cannot be determined.
Answer : b) 3.
Solution :
Let the number of lions in the Zoo be L and number of parrots be P.
Each lion has 4 legs and each parrot has 2 legs.
Therefore, Total number of legs of lions and parrots = 4L + 2P
Total number of heads = L + P
Given that, (4L + 2P) + 6 = 4(L + P)
4L + 2P + 6 = 4L + 4P
2P + 6 = 4P
2P = 6
P = number of parrots = 3.
Question 4
If in a group of dogs and crows, the number of heads is 24 and the number of feet is 70 then the number of crows will be:
a) 8 b) 13 c) none of these d) cannot be determined
Answer : b) 13.
Solution :
Let the number of dogs in the group be d and number of crows be c.
Total number of legs = 4d + 2c = 70 ...(1)
Total number of heads = d + c = 24 => 4d + 4c = 96......(2)
Now, Subtracting (2) from (1), we have, 2c = 96 - 70 = 26 => c = 13.
Hence, the required number of crows in the group is 13.
