__COMPARING QUANTITIES__

__COMPARING QUANTITIES__

**EXERCISE 9(A)**

**1.Express each of the following ratios in the simplest form:**

**(a) 3 kg 500 g : 4 kg 250 g**

**(b) 8 months : \( 1\dfrac{1}{2} \) years**

**(c) 36 minute : \( 1\dfrac{1}{2} \) hours**

**(d) 14 m : 7 m 35 cm**

**2.DIivide the number 952 into two parts in the ratio of 3 :5**

**3.A number is divided in the ratio 15 : 8 .If the second part is 56, find the number.**

**4.Convert the following into percentage:**

**(a) \( \dfrac{7}{10} \)**

**(b) 1 : 4**

**(c) 0.065**

**5.If 11.5% of a weight is 4.6 kg, find the weight.**

**6.If a number increases from 75 to 85, then find the percentage of increase.**

**7.If a weight of 65 kg is reduced to 60 kg, then find the percentage of reduction?**

**8.There are 56 teachers in a schools. Out of them 42 are female teachers and the rest are male teachers.Find the ratio of :**

**(a) Male teachers to the female teachers.**

**(b) Female teachers to the male teachers.**

**(c) Male teachers to the total numbers of teachers.**

**9.A boy secured 28% of 500 and failed in the examination by 10 marks.Find the pass marks percentage and the pass marks.**

**10.A cake weighting 1.98 kg is cut into two parts so that the first part is heavier than the second by 20%.Find the weight of each part.**

**11.The ratio of the length to the breadth of a rectangle is 5 : 3. If the perimeter of the rectangle is 144 m , what is the length of the rectangle ?**

**12.A fort had provisions for 150 mens for 45 days.After 10 days, 25 mens left the fort.How long will the food last at the same rate ?**

**13.A car covers 144 km in 3 hours.If an autorickshaw covers the same distance in 4 hour, find the ratio of the speed of the car to that of the autorickshaw ?**

**14.In a railway accident , 84 out of 525 passengers were injured.What % of the passengers were unhurt?**

**EXERCISE 9(B)**

**1.Find the S.P. when M.P. =₹ 990 and discount = 10%.**

**2.Find the M.P. when S.P. =₹ 990 and discount = 1%.**

**3.Find the discount, when M.P. = ₹1880 and S.P.= ₹1504.**

**4.A shopkeeper buys a shirt for ₹ 480. A girl buys it from him at a discount of \( 12\dfrac{1}{2} \)% on the market price of ₹600. Find the profit percent.**

**5.Amit purchased a flat for ₹ 7,56,000 and spent ₹ 44,000 on renovation .He sold it for ₹ 8,48,000.Find profit or loss percentage.**

**6.The catalogue price of an article is ₹ 16 , but the retailer is allowed a trade discount of 25% .At what price must the retailer sell it to gain 25% of what he pays for it ?**

**7.The price of a plate is slashed from ₹ 850 to ₹ 760 by a shopkeeper.Find the rate of discount.**

**8.The market price of a refrigerator is ₹ 15450. A dealer allows two successive discount at 15% and 8% . Find the selling price of refrigerator.**

**9.Find the single discount equivalent to successive discount of 13% and 15%.**

**10.How much percent above the cost should a dealer mark his goods so that after allowing a discount of 26% on the market price, he gains 20%.**

**EXERCISE 9(C)**

**1.An air conditioner is tested at ₹ 15000.What is the cost of the air conditioner to the customer, if he has to pay 5% as the sale tax?**

**2.An item is listed at ₹ 195.A sale tax @ 2% is added . What is the cost of the item to the customer?**

**3.Rahul purchased a coat for ₹ 1260 including tax of 5% VAT.What is the cost of the item before VAT was added?**

**4.An item is sold at ₹ 4995 in advise of 7% VAT. What is the cost of the item before VAT is added?**

**EXERCISE 9(D)**

**1.Find the compound interest on ₹ 6,500 in 3 years at 10% per annum compounded annually.**

**2.₹ 8000 is lent at 5% compound interest per year for 2 years.Find the amount and compound interest.**

**3.Find the amount & compound interest on ₹ 20,000 in \( 2\dfrac{1}{2} \) years at 10% per annum.**

**4.Amit deposited a sum of ₹ 50,000 in a bank for 2 years compounded half yearly at 10% per annum .Find the compound interest he gets.**

**5.Sumeet borrowed ₹ 36,000 from a financier at 25% per annum compounded half yearly.What amount of money will discharge his debt after \( \dfrac{1}{2} \) years?**

**6.Find the difference between the simple interest and compound interest on ₹ 1,500 for 3 years at 5% per annum.**

**7.A man invests ₹ 30,800 at 5% per annum compound interest for 3 year.Calculate:**

**(a) The interest for the first year.**

**(b) The amount standing to his credit at the end of the second year.**

**(c) The interest for the third year.**

**EXERCISE 9(E)**

**1.How much will ₹ 25,000 amount to in 3 years, compounded yearly, if the rates for the successive years are 6%, 8% and 10% respectively.**

**2.A man borrowed a sum of money and agrees to pay off by paying ₹ 6300 at the end of the first year and ₹ 8820 at the end of the second year.If the rate of the compound interest is 5% per annum, find the sum borrowed.**

**3.Calculate the amount and compound interest on ₹ 10,000 for 3 years at 2% per annum.**

**4.Find the amount of ₹ 12500 for 2 years compounded annually, the rate of interest being 15% for the first year and 16% for the second year.**

**5.Find the compound interest on ₹ 14000 at 16% per annum for \( 2\dfrac{3}{4} \) years.**

**EXERCISE 9(F)**

**1.Find the amount and the compound interest on ₹ 50000 for 2 years at 2% per annum compounded half yearly.**

**2.Find the compound interest on ₹ 5000 for \( 2\dfrac{1}{2} \) years at 5% per annum, compounded half yearly.**

**3.A sum of money is lent out at compound interest for 2 years at 20% per annum , compound interest begin reckoned yearly.**

**If the same sum of money was lent out at compound interest at the same rate per annum, compound interest begin reckoned half yearly it would have fetched ₹ 482 more by way of interest.Calculate the sum of money lent out.**

**4.What is the difference between the amount on ₹ 50,000 for \( 1\dfrac{1}{2} \) years at 4% per annum compound yearly and half yearly ?**

**EXERCISE 9(G)**

**1.What sum of money will amount to ₹ 3630 in 2 years at 10% per annum compound interest ?**

**2.On what sum of money will the compound interest for 2 years at 8% per annum be ₹ 3744 ?**

**3.The simple interest on a certain sum for 3 years at 15% is ₹ 9900.Find the compound interest for same time and same rate of interest ?**

**4.The difference between the compound interest and the single interest on a certain sum at 11% per annum for 2 years is ₹ 36. Find the sum.**

**5.The simple interest on this sum of money for 2 years at 4% per annum is ₹ 340.Find **

**(a) The sum of money.**

**(b) The compound interest on this sum for one year payable half yearly at the same rate.**

**6.At what rate per cent compound interest per annum will ₹ 6250 amount to ₹ 720 in 2 years ?**

**7.In what time will ₹ 800 amount to ₹ 882 at 5% rate per annum compounded annually ?**