Q. 1 (a) Calculate Ushr on a
rice crop by natural resources amounting to Rs.9,30,000. (10)
(b) Calculate Zakat on gold amounting to Rs.13,50,000. (10)
(a) To calculate Ushr on a rice
crop, the Ushr rate needs to be determined. The Ushr rate for agricultural
produce varies based on factors such as the type of crop and the region. Let's
assume the Ushr rate for rice crop in this scenario is 10%.
Ushr amount = (Total crop value) x
(Ushr rate)
Given that the natural resources
amount to Rs. 9,30,000:
Ushr amount = Rs. 9,30,000 x 0.10
Ushr amount = Rs. 93,000
Therefore, the Ushr on the rice
crop by natural resources amounts to Rs. 93,000.
(b) To calculate Zakat on gold, the
Zakat rate for gold needs to be determined. The Zakat rate for gold is
typically 2.5%.
Zakat amount = (Total gold value) x
(Zakat rate)
Given that the gold amount is Rs.
13,50,000:
Zakat amount = Rs. 13,50,000 x
0.025
Zakat amount = Rs. 33,750
Therefore, the Zakat on gold
amounting to Rs. 13,50,000 is Rs. 33,750.
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Q. 2 (a) If the stay of 12 men
for 7 days in a hotel cost Rs.20,500. Find the cost for the stay of 10 men for
8 days. (10)
(b) Two angles in a triangle are 45o
and 75o. Find the ratio of the third angle to the sum of the first
two angles. (10)
(a) To
find the cost for the stay of 10 men for 8 days, we can use the concept of
proportionality.
Let's
assume the cost for the stay of 10 men for 8 days is C.
According
to the given information, the cost for the stay of 12 men for 7 days is Rs.
20,500.
We can
set up a proportion based on the number of men and the number of days:
12 men /
7 days = 10 men / 8 days
Cross-multiplying,
we get:
12 men *
8 days = 10 men * 7 days
96
men-days = 70 men-days
Now, we
can calculate the cost for the stay of 10 men for 8 days:
C = (Cost
for 12 men for 7 days * 70 men-days) / 96 men-days
C = (Rs.
20,500 * 70) / 96
C = Rs.
14,979.17 (approx.)
Therefore,
the cost for the stay of 10 men for 8 days is approximately Rs. 14,979.17.
(b) The
sum of the angles in a triangle is always 180 degrees.
Let's
assume the third angle in the triangle is A.
Given
that two angles in the triangle are 45 degrees and 75 degrees:
Third
angle = 180 degrees - (45 degrees + 75 degrees)
Third
angle = 180 degrees - 120 degrees
Third
angle = 60 degrees
Now, we
can find the ratio of the third angle to the sum of the first two angles:
Ratio =
Third angle / (Sum of first two angles)
Ratio =
60 degrees / (45 degrees + 75 degrees)
Ratio =
60 degrees / 120 degrees
Ratio =
0.5
Therefore,
the ratio of the third angle to the sum of the first two angles is 0.5.
Q. 3 (a) The
marked price of a wall clock is Rs.900. The shopkeeper offers a discount of 5%
and still gains 10%. Find the price at which the shopkeeper purchased it. (10)
(b) Divide Rs.18,400 in three friends such that the
ratio of their parts is 3:6:8. (10)
(a) To
find the price at which the shopkeeper purchased the wall clock, we can use the
concept of successive discounts and gains.
Let's
assume the cost price of the wall clock is C.
Given
that the marked price of the wall clock is Rs. 900 and the shopkeeper offers a
discount of 5%. This means the shopkeeper sells the wall clock for 95% of the
marked price.
First
discount price = (95% of the marked price) = 0.95 * Rs. 900 = Rs. 855
Now, we
are told that the shopkeeper still gains 10%. This means the selling price is
110% of the cost price.
Selling
price = (110% of the cost price) = 1.10 * C
Since the
shopkeeper sells the wall clock for Rs. 855, we can equate the selling price to
Rs. 855:
1.10 * C
= Rs. 855
Now, we
can solve for C:
C = Rs.
855 / 1.10
C ≈ Rs.
777.27 (approx.)
Therefore,
the price at which the shopkeeper purchased the wall clock is approximately Rs.
777.27.
(b) To
divide Rs. 18,400 among three friends in the ratio of 3:6:8, we need to
determine the parts allocated to each friend.
The total
ratio is 3 + 6 + 8 = 17.
Let's
assume the common ratio factor is x.
The parts
allocated to each friend can be calculated as follows:
Friend 1:
(3/17) * Rs. 18,400 = Rs. (3/17) * 18,400 = Rs. 3,200
Friend 2:
(6/17) * Rs. 18,400 = Rs. (6/17) * 18,400 = Rs. 6,400
Friend 3:
(8/17) * Rs. 18,400 = Rs. (8/17) * 18,400 = Rs. 8,800
Therefore,
the parts allocated to the three friends in the ratio of 3:6:8 are Rs. 3,200,
Rs. 6,400, and Rs. 8,800, respectively.
Q. 4 (a) At what annual rate of profit would a sum of
Rs.780 will increase to Rs.1340 in 2 years 3 months? (10)
(b) Find
the compound profit on Rs.3000 for 2
years at 4%. (10)
(a) To
calculate the annual rate of profit, we can use the formula for compound
interest:
Amount =
Principal * (1 + Rate/100)^Time
Given
that a sum of Rs. 780 increases to Rs. 1340 in 2 years 3 months (or 2.25
years), we can calculate the annual rate of profit.
Principal
= Rs. 780
Amount =
Rs. 1340
Time =
2.25 years
Using the
compound interest formula, we have:
Rs. 1340
= Rs. 780 * (1 + Rate/100)^2.25
Dividing
both sides of the equation by Rs. 780:
(1340/780)
= (1 + Rate/100)^2.25
Taking
the square root of both sides:
sqrt(1340/780)
= 1 + Rate/100
Calculating
the square root and simplifying:
1.0838 ≈
1 + Rate/100
Subtracting
1 from both sides:
0.0838 ≈
Rate/100
Rate ≈
8.38%
Therefore,
the annual rate of profit would be approximately 8.38%.
(b) To
calculate the compound interest on Rs. 3000 for 2 years at 4%, we can use the
compound interest formula:
Compound
Interest = Principal * [(1 + Rate/100)^Time - 1]
Principal
= Rs. 3000
Rate = 4%
Time = 2
years
Using the
compound interest formula, we have:
Compound
Interest = Rs. 3000 * [(1 + 4/100)^2 - 1]
Compound
Interest = Rs. 3000 * [(1.04)^2 - 1]
Compound
Interest = Rs. 3000 * [1.0816 - 1]
Compound
Interest = Rs. 3000 * 0.0816
Compound
Interest ≈ Rs. 244.80
Therefore,
the compound interest on Rs. 3000 for 2 years at 4% is approximately Rs.
244.80.
Q. 5 (a) The
price of a motorcycle is Rs.4000. If 9% sales tax is charged, then calculate
the amount of sales tax on 25 such motorcycles. (10)
(b) If gross pay of a person is Rs.650,000,
then calculate his net take home salary, after deductions of Rs.380 as income
tax, Rs.700 as benevolent fund, Rs.2100 as G.P fund and Rs.250 as group
insurance. (10)
(a) To
calculate the amount of sales tax on 25 motorcycles, we first need to find the
sales tax for one motorcycle and then multiply it by 25.
Given
that the price of one motorcycle is Rs. 4000 and the sales tax rate is 9%:
Sales tax
for one motorcycle = 9% of Rs. 4000
Sales tax
for one motorcycle = (9/100) * Rs. 4000
Sales tax
for one motorcycle = Rs. 360
Now, to
calculate the sales tax on 25 motorcycles, we multiply the sales tax for one
motorcycle by 25:
Sales tax
on 25 motorcycles = Rs. 360 * 25
Sales tax
on 25 motorcycles = Rs. 9,000
Therefore,
the amount of sales tax on 25 motorcycles would be Rs. 9,000.
(b) To
calculate the net take-home salary after deductions, we subtract the deductions
from the gross pay.
Given:
Gross pay
= Rs. 650,000
Income
tax deduction = Rs. 380
Benevolent
fund deduction = Rs. 700
G.P. fund
deduction = Rs. 2100
Group
insurance deduction = Rs. 250
Net
take-home salary = Gross pay - (Income tax + Benevolent fund + G.P. fund + Group
insurance)
Net
take-home salary = Rs. 650,000 - (Rs. 380 + Rs. 700 + Rs. 2100 + Rs. 250)
Net
take-home salary = Rs. 650,000 - Rs. 3430
Net
take-home salary = Rs. 646,570
Therefore,
the net take-home salary, after deductions, would be Rs. 646,570.
Dear Student,
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