Ratio, Proportion and Variation

In a college, the ratio of the number of students studying in Arts, Commerce and Science was $3:5:8$ respectively. If the number of the students in these streams be increased by $20\%, 40\%$ and $25\%$ respectively, the new ratio of the number of students in these streams will be?

A piece of cloth is cut into pieces in the ratio of $3:5$ by length. The longer of the two is further cut in the ratio of $5:6$ by length. What is the ratio of each of the three pieces?

Populations of two villages X and Y are in the ratio of 5 : 7 respectively. If the population of village Y increases by 25000 and the population of village X remains unchanged the respective ratio of their populations becomes 25:36. What is the population of village X ?

The ratio of the prices of two houses A and B was 4 : 5 last year. This year, the price of A is increased by 25% and that of B by Rs.50000. If their prices are now in the ratio 9 : 10, the price of A last year was-

What ratio must a lab technician mix methane worth Rs. 60 a kg and Ethane worth Rs. 65 a kg so that by selling this compound mixture at Rs. 68.20 a kg, he may gain 10%?

Pratul's monthly income is four-fifth of Ravi's montly income. Ravi's monthly income is Rs. 36,000. What is Pratul's annual income ?

Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40:57. What is Sumit’s present salary?

In a piggy bank there are 1 rupee. 50 paise and 25 paise coins. The respective ratio of their numbers is 10 : 8 : 5. In piggy bank there is a total sum of Rs.976. How many 25 piggy coins are there in the piggy bank?

Vishal invested part of his monthly income in sotcks share and that of  part in mutual fund. He spent the remaining amount on domestic needs and apparel in the ratio 5 : 3 respectively. The expenditure on domestic needs was Rs. 2100. What is his annual income ?

A man pays $₹6.4$per $\mathrm{litre}$ of apple juice. He adds water and sells the mixture at $₹8$ per$\mathrm{litre}$, thereby making $37.5\%$profit. Find the proportion of the water to that of the apple juice received by the customers.

$Rs.117$ was to be distributed between $A, B, \& C$ in the ratio of $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ but it was distributed in the ratio of $2:3:4$ by mistake So, who was benefited the most & hour much more did he get?

The number of employees in companies A, B and C are in a ratio of 3 : 2 : 4 respectively. If the number of employees in the three companies is increased by 20%, 30% and 15% respectively, what will be the new ratio of employees working in companies A, B and C respectively ?

The number of employees in companies A, B and C are in a ratio of 3 : 2 : 4 respectively. If the number of employees in the three companies is increased by 20%, 30% and 15% respectively, what will be the new ratio of employees working in companies A, B and C respectively ?

Pure milk costs Rs. 16 per litre. After adding water the milkman sells the mixture Rs. 15 per litre and thereby makes a profit of 25%. In what respective ratio does he mix milk with water?

Pure milk costs Rs. 16 per litre. After adding water the milkman sells the mixture Rs. 15 per litre and thereby makes a profit of 25%. In what respective ratio does he mix milk with water?

If the length of a rectangle is increased in the ratio 6 : 7 and its breadth is diminished in the raio 5 : 4 then its area will be diminished in the ratio

If the length of a rectangle is increased in the ratio 6 : 7 and its breadth is diminished in the raio 5 : 4 then its area will be diminished in the ratio

People from West Bengal eat rice, corn and wheat in the ratio $5:2:3$ while the people from Uttar Pradesh eat in the ratio $4:1:7.$ A person from West Bengal bought $58 \mathrm{kg}$ of food items while the person from Uttar Pradesh bought $66 \mathrm{kg}$ of food items. Calculate the ratio of rice and corn bought by the person from Uttar Pradesh and Rice and Wheat bought by person from West Bengal?

Three containers A, B and C contain wine and water in the respective ratios of $5:7, 7:9$ and $4:5.$ Each container has an equal volume of the mixture. If a man took two-thirds of the quantity from container A, four-fifths of the quantity from container B and half the quantity from container C and mixed in another container D, what is the ratio of wine to water in container D?

In an annual exam of five subjects, a student's scores were in the proportion of $7:8:9:10:11$. If the maximum marks in each subject are $200$ and he scores $60\%$ overall, then in how many papers he scored more than $55\%$ marks?